A300194 -id:A300194 - cp's OEIS frontend

A300196 Coefficients of non-constant terms of a Calabi-Yau modular form attached to 4-dimensional Dwork family.

11, 115137, 2265573692, 54820079452449, 1477052190387154386, 42523861222488896739828, 1280632628533246391347932600, 39845698655955128983429884963873, 1270798742041866157250422963241434559, 41323333497425826763780540687931705198262

Offset: 1

Younes Nikdelan, Mar 22 2018

nonn

The 8-tuple (1/36 + 20*A300194, -1 +216*A300195, -1/36 + 14*A300196, -1/6 + 24*A300197, -1/72 + 2*A300198, -1/46656 * A300199, 1/36 - 2*A300200,  -1/7776 + 7/18 * A300201)  gives a solution of the modular vector field R = Sum_{i=1..8} R_i d/dt_i on the enhanced moduli space arising from 4-dimensional Dwork family, where d/dt_i's give the standard basis of the tangent space in the chart (t_1,t_2,...,t_8) and
R_1 = -t_1*t_2+t_3;
R_2 = (-t_1^6*t_2^2+1/36*t_3^2*t_4*t_8+t_2^2*t_6)/(t_1^6-t_6);
R_3 = (-3*t_1^6*t_2*t_3+1/36*t_3^2*t_5*t_8+3*t_2*t_3*t_6)/(t_1^6-t_6);
R_4 = (-t_1^6*t_2*t_4-1/36*t_3^2*t_7*t_8+t_2*t_4*t_6)/(t_1^6-t_6);
R_5 = (-2*t_1^6*t_3*t_4-4*t_1^6*t_2*t_5+5*t_1^4*t_3*t_8+1/36*t_3*t_5^2*t_8+ 2*t_3*t_4*t_6+4*t_2*t_5*t_6)/(2*(t_1^6-t_6));
R_6 = -6*t_2*t_6;
R_7 = -18*t_1^2+1/2*t_4^2;
R_8 = (-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8)/(t_1^6-t_6);
For more details see the Movasati & Nikdelan link Section 8.3.

H. Movasati, Y. Nikdelan, Gauss-Manin Connection in Disguise: Dwork Family, arXiv:1603.09411 [math.AG], 2016-2017. See Table 2, (1/14)*t_3.
H. Movasati, Foliation.lib.

Cf. A300194, A300195, A300197, A300198, A300199, A300200, A300201.

// This program has to be compiled in SINGULAR. By changing "int iter" you can
// calculate more coefficients. Note that this program is using a library calling
// "foliation.lib" written by H. Movasati, which is available in the link given in
// LINKS section as Foliation.lib.
LIB "linalg.lib"; LIB "foliation.lib";
ring r=0, (t_1,t_2,t_3,t_4,t_5,t_6,t_7,t_8,q),dp;
int pm=1;number t10=1/36;number ko=1/216;number c4=ko^2;number t20=-1;number t81=49/18;number a=-6*t20;
poly dis=t_1^6-t_6;
poly dt1=dis*(-t_1*t_2+t_3);
poly dt2=(1296*c4*t_3^2*t_4*t_8-t_1^6*t_2^2+t_2^2*t_6);
poly dt3=(1296*c4*t_3^2*t_5*t_8-3*t_1^6*t_2*t_3+3*t_2*t_3*t_6);
poly dt4=(-1296*c4*t_3^2*t_7*t_8-t_1^6*t_2*t_4+t_2*t_4*t_6);
poly dt5=(1296*c4*t_3*t_5^2*t_8-4*t_1^6*t_2*t_5-2*t_1^6*t_3*t_4+5*t_1^4*t_3*t_8+4*t_2*t_5*t_6+2*t_3*t_4*t_6)/(2);
poly dt6=dis*(-6*t_2*t_6);
poly dt7=dis*((1296*c4*t_4^2-t_1^2)/(2592*c4));
poly dt8=(-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8);
list pose;
pose=(60*ko)/(49*t10^2)*t81*q+(t10),(-162*t20*ko)/(49*t10^3)*t81*q+(t20),(-66*t20*ko)/(7*t10^2)*t81*q+(t10*t20),16/(147*t10^2)*t81*q+(-t10)/(36*ko),45/(49*t10)*t81*q+(-t10^2)/(12*ko),(3888*t10^3*ko)/49*t81*q,1/(1512*t10*t20*ko)*t81*q+(-t10^2)/(1296*t20*ko^2),t81*q+(-t10^3)/(36*ko);
list vecfield=dt1,dt2,dt3,dt4,dt5,dt6,dt7,dt8;
list denomv=dis,dis,dis,dis,dis,dis,dis,dis;
intvec upto=1,1,1,1,1,1,1,1;intvec whichpow;
int iter=20;
int n;
for (n=2; n<=iter;n=n+1){upto=n,n,n,n,n,n,n,n; whichpow=upto;pose=qexpansion(vecfield,denomv,pose,upto,upto,a); n;}
1/14*pose[3]+1/504;

A300199 Coefficients of non-constant terms of a Calabi-Yau modular form attached to 4-dimensional Dwork family.

Original entry on oeis.org

-1, 1944, 10066356, 139857401664, 2615615263199250, 57453864811412558112, 1396383637688295560244360, 36387737129455500217143965184, 997805935308219028231096155360699, 28447809694713927701484542997198258000

Offset: 1

Younes Nikdelan, Mar 22 2018

sign

The 8-tuple (1/36 + 20*A300194, -1 + 216*A300195, -1/36 + 14*A300196, -1/6 + 24*A300197, -1/72 + 2*A300198, -1/46656 * A300199, 1/36 - 2*A300200,  -1/7776 + 7/18 * A300201) gives a solution of the modular vector field R = Sum_{i=1..8} R_i d/dt_i on the enhanced moduli space arising from 4-dimensional Dwork family, where d/dt_i's give the standard basis of the tangent space in the chart (t_1,t_2,...,t_8) and
R_1 = -t_1*t_2+t_3;
R_2 = (-t_1^6*t_2^2+1/36*t_3^2*t_4*t_8+t_2^2*t_6)/(t_1^6-t_6);
R_3 = (-3*t_1^6*t_2*t_3+1/36*t_3^2*t_5*t_8+3*t_2*t_3*t_6)/(t_1^6-t_6);
R_4 = (-t_1^6*t_2*t_4-1/36*t_3^2*t_7*t_8+t_2*t_4*t_6)/(t_1^6-t_6);
R_5 = (-2*t_1^6*t_3*t_4-4*t_1^6*t_2*t_5+5*t_1^4*t_3*t_8+1/36*t_3*t_5^2*t_8+ 2*t_3*t_4*t_6+4*t_2*t_5*t_6)/(2*(t_1^6-t_6));
R_6 = -6*t_2*t_6;
R_7 = -18*t_1^2+1/2*t_4^2;
R_8 = (-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8)/(t_1^6-t_6);
For more details see the Movasati & Nikdelan link Section 8.3.

H. Movasati, Y. Nikdelan, Gauss-Manin Connection in Disguise: Dwork Family, arXiv:1603.09411 [math.AG], 2016-2017. See Table 2, (-6^6)*t_6.
H. Movasati, Foliation.lib.

Cf. A300194, A300195, A300196, A300197, A300198, A300200, A300201.

// This program has to be compiled in SINGULAR. By changing "int iter" you can
// calculate more coefficients. Note that this program is using a library calling
// "foliation.lib" written by H. Movasati, which is available in the link given in
// LINKS section as Foliation.lib.
LIB "linalg.lib"; LIB "foliation.lib";
ring r=0, (t_1,t_2,t_3,t_4,t_5,t_6,t_7,t_8,q),dp;
int pm=1;number t10=1/36;number ko=1/216;number c4=ko^2;number t20=-1;number t81=49/18;number a=-6*t20;
poly dis=t_1^6-t_6;
poly dt1=dis*(-t_1*t_2+t_3);
poly dt2=(1296*c4*t_3^2*t_4*t_8-t_1^6*t_2^2+t_2^2*t_6);
poly dt3=(1296*c4*t_3^2*t_5*t_8-3*t_1^6*t_2*t_3+3*t_2*t_3*t_6);
poly dt4=(-1296*c4*t_3^2*t_7*t_8-t_1^6*t_2*t_4+t_2*t_4*t_6);
poly dt5=(1296*c4*t_3*t_5^2*t_8-4*t_1^6*t_2*t_5-2*t_1^6*t_3*t_4+5*t_1^4*t_3*t_8+4*t_2*t_5*t_6+2*t_3*t_4*t_6)/(2);
poly dt6=dis*(-6*t_2*t_6);
poly dt7=dis*((1296*c4*t_4^2-t_1^2)/(2592*c4));
poly dt8=(-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8);
list pose;
pose=(60*ko)/(49*t10^2)*t81*q+(t10),(-162*t20*ko)/(49*t10^3)*t81*q+(t20),(-66*t20*ko)/(7*t10^2)*t81*q+(t10*t20),16/(147*t10^2)*t81*q+(-t10)/(36*ko),45/(49*t10)*t81*q+(-t10^2)/(12*ko),(3888*t10^3*ko)/49*t81*q,1/(1512*t10*t20*ko)*t81*q+(-t10^2)/(1296*t20*ko^2),t81*q+(-t10^3)/(36*ko);
list vecfield=dt1,dt2,dt3,dt4,dt5,dt6,dt7,dt8;
list denomv=dis,dis,dis,dis,dis,dis,dis,dis;
intvec upto=1,1,1,1,1,1,1,1;intvec whichpow;
int iter=20;
int n;
for (n=2; n<=iter;n=n+1){upto=n,n,n,n,n,n,n,n; whichpow=upto;pose=qexpansion(vecfield,denomv,pose,upto,upto,a); n;}
-6^6*pose[6];

A300195 Coefficients of non-constant terms of a Calabi-Yau modular form attached to 4-dimensional Dwork family.

Original entry on oeis.org

9, 110703, 2248267748, 55181044614231, 1498877559908208054, 43378802521495632926652, 1311174697901836067695479240, 40906572130277189636181364125927, 1307352158741343902327517216908624501, 42582208719047972481638285517019993624218

Offset: 1

Younes Nikdelan, Mar 16 2018

nonn

The 8-tuple (1/36 + 20*A300194, -1 + 216*A300195, -1/36 + 14*A300196, -1/6 + 24*A300197, -1/72 + 2*A300198, -1/46656 * A300199, 1/36 - 2*A300200, -1/7776 + 7/18 * A300201) gives a solution of the modular vector field R = Sum_{i=1..8} R_i d/dt_i on the enhanced moduli space arising from 4-dimensional Dwork family, where d/dt_i's give the standard basis of the tangent space in the chart (t_1,t_2,...,t_8) and
R_1 = -t_1*t_2+t_3;
R_2 = (-t_1^6*t_2^2+1/36*t_3^2*t_4*t_8+t_2^2*t_6)/(t_1^6-t_6);
R_3 = (-3*t_1^6*t_2*t_3+1/36*t_3^2*t_5*t_8+3*t_2*t_3*t_6)/(t_1^6-t_6);
R_4 = (-t_1^6*t_2*t_4-1/36*t_3^2*t_7*t_8+t_2*t_4*t_6)/(t_1^6-t_6);
R_5 = (-2*t_1^6*t_3*t_4-4*t_1^6*t_2*t_5+5*t_1^4*t_3*t_8+1/36*t_3*t_5^2*t_8+ 2*t_3*t_4*t_6+4*t_2*t_5*t_6)/(2*(t_1^6-t_6));
R_6 = -6*t_2*t_6;
R_7 = -18*t_1^2+1/2*t_4^2;
R_8 = (-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8)/(t_1^6-t_6);
For more details see the Movasati & Nikdelan link Section 8.3.

H. Movasati, Y. Nikdelan, Gauss-Manin Connection in Disguise: Dwork Family, arXiv:1603.09411 [math.AG], 2016-2017. See Table 2, (1/216)*t_2.
H. Movasati, Foliation.lib.

Cf. A300194, A300196, A300197, A300198, A300199, A300200, A300201.

// This program has to be compiled in SINGULAR. By changing "int iter" you can
// calculate more coefficients. Note that this program is using a library calling
// "foliation.lib" written by H. Movasati, which is available in the link given in
// LINKS section as Foliation.lib.
LIB "linalg.lib"; LIB "foliation.lib";
ring r=0, (t_1,t_2,t_3,t_4,t_5,t_6,t_7,t_8,q),dp;
int pm=1;number t10=1/36;number ko=1/216;number c4=ko^2;number t20=-1;number t81=49/18;number a=-6*t20;
poly dis=t_1^6-t_6;
poly dt1=dis*(-t_1*t_2+t_3);
poly dt2=(1296*c4*t_3^2*t_4*t_8-t_1^6*t_2^2+t_2^2*t_6);
poly dt3=(1296*c4*t_3^2*t_5*t_8-3*t_1^6*t_2*t_3+3*t_2*t_3*t_6);
poly dt4=(-1296*c4*t_3^2*t_7*t_8-t_1^6*t_2*t_4+t_2*t_4*t_6);
poly dt5=(1296*c4*t_3*t_5^2*t_8-4*t_1^6*t_2*t_5-2*t_1^6*t_3*t_4+5*t_1^4*t_3*t_8+4*t_2*t_5*t_6+2*t_3*t_4*t_6)/(2);
poly dt6=dis*(-6*t_2*t_6);
poly dt7=dis*((1296*c4*t_4^2-t_1^2)/(2592*c4));
poly dt8=(-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8);
list pose;
pose=(60*ko)/(49*t10^2)*t81*q+(t10),(-162*t20*ko)/(49*t10^3)*t81*q+(t20),(-66*t20*ko)/(7*t10^2)*t81*q+(t10*t20),16/(147*t10^2)*t81*q+(-t10)/(36*ko),45/(49*t10)*t81*q+(-t10^2)/(12*ko),(3888*t10^3*ko)/49*t81*q,1/(1512*t10*t20*ko)*t81*q+(-t10^2)/(1296*t20*ko^2),t81*q+(-t10^3)/(36*ko);
list vecfield=dt1,dt2,dt3,dt4,dt5,dt6,dt7,dt8;
list denomv=dis,dis,dis,dis,dis,dis,dis,dis;
intvec upto=1,1,1,1,1,1,1,1;intvec whichpow;
int iter=20;
int n;
for (n=2; n<=iter;n=n+1){upto=n,n,n,n,n,n,n,n; whichpow=upto;pose=qexpansion(vecfield,denomv,pose,upto,upto,a); n;}
1/216*pose[2]+1/216;

A300197 Coefficients of non-constant terms of a Calabi-Yau modular form attached to 4-dimensional Dwork family.

Original entry on oeis.org

16, 193131, 3904146832, 95619949713765, 2594164605185043648, 75018247757143686903060, 2266261629414347188622815776, 70674869456542669855003845042969, 2258019930744219211729662533571321808, 73528348542628960335141142217651558123754

Offset: 1

Younes Nikdelan, Mar 22 2018

nonn

The 8-tuple (1/36 + 20*A300194, -1 + 216*A300195, -1/36 + 14*A300196, -1/6 + 24*A300197, -1/72 + 2*A300198, -1/46656 * A300199, 1/36 - 2*A300200, -1/7776 + 7/18 * A300201) gives a solution of the modular vector field R = Sum_{i=1..8} R_i d/dt_i on the enhanced moduli space arising from 4-dimensional Dwork family, where d/dt_i's give the standard basis of the tangent space in the chart (t_1,t_2,...,t_8) and
R_1 = -t_1*t_2+t_3;
R_2 = (-t_1^6*t_2^2+1/36*t_3^2*t_4*t_8+t_2^2*t_6)/(t_1^6-t_6);
R_3 = (-3*t_1^6*t_2*t_3+1/36*t_3^2*t_5*t_8+3*t_2*t_3*t_6)/(t_1^6-t_6);
R_4 = (-t_1^6*t_2*t_4-1/36*t_3^2*t_7*t_8+t_2*t_4*t_6)/(t_1^6-t_6);
R_5 = (-2*t_1^6*t_3*t_4-4*t_1^6*t_2*t_5+5*t_1^4*t_3*t_8+1/36*t_3*t_5^2*t_8+ 2*t_3*t_4*t_6+4*t_2*t_5*t_6)/(2*(t_1^6-t_6));
R_6 = -6*t_2*t_6;
R_7 = -18*t_1^2+1/2*t_4^2;
R_8 = (-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8)/(t_1^6-t_6);
For more details see the Movasati & Nikdelan link Section 8.3.

H. Movasati, Y. Nikdelan, Gauss-Manin Connection in Disguise: Dwork Family, arXiv:1603.09411 [math.AG], 2016-2017. See Table 2, (1/24)*t_4.
H. Movasati, Foliation.lib.

Cf. A300194, A300195, A300196, A300198, A300199, A300200, A300201.

// This program has to be compiled in SINGULAR. By changing "int iter" you can
// calculate more coefficients. Note that this program is using a library calling
// "foliation.lib" written by H. Movasati, which is available in the link given in
// LINKS section as Foliation.lib.
LIB "linalg.lib"; LIB "foliation.lib";
ring r=0, (t_1,t_2,t_3,t_4,t_5,t_6,t_7,t_8,q),dp;
int pm=1;number t10=1/36;number ko=1/216;number c4=ko^2;number t20=-1;number t81=49/18;number a=-6*t20;
poly dis=t_1^6-t_6;
poly dt1=dis*(-t_1*t_2+t_3);
poly dt2=(1296*c4*t_3^2*t_4*t_8-t_1^6*t_2^2+t_2^2*t_6);
poly dt3=(1296*c4*t_3^2*t_5*t_8-3*t_1^6*t_2*t_3+3*t_2*t_3*t_6);
poly dt4=(-1296*c4*t_3^2*t_7*t_8-t_1^6*t_2*t_4+t_2*t_4*t_6);
poly dt5=(1296*c4*t_3*t_5^2*t_8-4*t_1^6*t_2*t_5-2*t_1^6*t_3*t_4+5*t_1^4*t_3*t_8+4*t_2*t_5*t_6+2*t_3*t_4*t_6)/(2);
poly dt6=dis*(-6*t_2*t_6);
poly dt7=dis*((1296*c4*t_4^2-t_1^2)/(2592*c4));
poly dt8=(-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8);
list pose;
pose=(60*ko)/(49*t10^2)*t81*q+(t10),(-162*t20*ko)/(49*t10^3)*t81*q+(t20),(-66*t20*ko)/(7*t10^2)*t81*q+(t10*t20),16/(147*t10^2)*t81*q+(-t10)/(36*ko),45/(49*t10)*t81*q+(-t10^2)/(12*ko),(3888*t10^3*ko)/49*t81*q,1/(1512*t10*t20*ko)*t81*q+(-t10^2)/(1296*t20*ko^2),t81*q+(-t10^3)/(36*ko);
list vecfield=dt1,dt2,dt3,dt4,dt5,dt6,dt7,dt8;
list denomv=dis,dis,dis,dis,dis,dis,dis,dis;
intvec upto=1,1,1,1,1,1,1,1;intvec whichpow;
int iter=20;
int n;
for (n=2; n<=iter;n=n+1){upto=n,n,n,n,n,n,n,n; whichpow=upto;pose=qexpansion(vecfield,denomv,pose,upto,upto,a); n;}
1/24*pose[4]+1/144;

A300198 Coefficients of non-constant terms of a Calabi-Yau modular form attached to 4-dimensional Dwork family.

Original entry on oeis.org

45, 469872, 9215455916, 222628516313454, 5992746995783064438, 172421735348939185816992, 5190295355475474691505991096, 161438078857853783804701774555530, 5147432171207325946295914462556988257, 167348179641043887251862298724868852231264

Offset: 1

Younes Nikdelan, Mar 22 2018

nonn

The 8-tuple (1/36 + 20*A300194, -1 + 216*A300195, -1/36 + 14*A300196, -1/6 + 24*A300197, -1/72 + 2*A300198, -1/46656 * A300199, 1/36 - 2*A300200, -1/7776 + 7/18 * A300201) gives a solution of the modular vector field R = Sum_{i=1..8} R_i d/dt_i on the enhanced moduli space arising from 4-dimensional Dwork family, where d/dt_i's give the standard basis of the tangent space in the chart (t_1,t_2,...,t_8) and
R_1 = -t_1*t_2+t_3;
R_2 = (-t_1^6*t_2^2+1/36*t_3^2*t_4*t_8+t_2^2*t_6)/(t_1^6-t_6);
R_3 = (-3*t_1^6*t_2*t_3+1/36*t_3^2*t_5*t_8+3*t_2*t_3*t_6)/(t_1^6-t_6);
R_4 = (-t_1^6*t_2*t_4-1/36*t_3^2*t_7*t_8+t_2*t_4*t_6)/(t_1^6-t_6);
R_5 = (-2*t_1^6*t_3*t_4-4*t_1^6*t_2*t_5+5*t_1^4*t_3*t_8+1/36*t_3*t_5^2*t_8+ 2*t_3*t_4*t_6+4*t_2*t_5*t_6)/(2*(t_1^6-t_6));
R_6 = -6*t_2*t_6;
R_7 = -18*t_1^2+1/2*t_4^2;
R_8 = (-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8)/(t_1^6-t_6);
For more details see the Movasati & Nikdelan link Section 8.3.

H. Movasati, Y. Nikdelan, Gauss-Manin Connection in Disguise: Dwork Family, arXiv:1603.09411 [math.AG], 2016-2017. See Table 2, (1/2)*t_5.
H. Movasati, Foliation.lib.

Cf. A300194, A300195, A300196, A300197, A300199, A300200, A300201.

// This program has to be compiled in SINGULAR. By changing "int iter" you can
// calculate more coefficients. Note that this program is using a library calling
// "foliation.lib" written by H. Movasati, which is available in the link given in
// LINKS section as Foliation.lib.
LIB "linalg.lib"; LIB "foliation.lib";
ring r=0, (t_1,t_2,t_3,t_4,t_5,t_6,t_7,t_8,q),dp;
int pm=1;number t10=1/36;number ko=1/216;number c4=ko^2;number t20=-1;number t81=49/18;number a=-6*t20;
poly dis=t_1^6-t_6;
poly dt1=dis*(-t_1*t_2+t_3);
poly dt2=(1296*c4*t_3^2*t_4*t_8-t_1^6*t_2^2+t_2^2*t_6);
poly dt3=(1296*c4*t_3^2*t_5*t_8-3*t_1^6*t_2*t_3+3*t_2*t_3*t_6);
poly dt4=(-1296*c4*t_3^2*t_7*t_8-t_1^6*t_2*t_4+t_2*t_4*t_6);
poly dt5=(1296*c4*t_3*t_5^2*t_8-4*t_1^6*t_2*t_5-2*t_1^6*t_3*t_4+5*t_1^4*t_3*t_8+4*t_2*t_5*t_6+2*t_3*t_4*t_6)/(2);
poly dt6=dis*(-6*t_2*t_6);
poly dt7=dis*((1296*c4*t_4^2-t_1^2)/(2592*c4));
poly dt8=(-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8);
list pose;
pose=(60*ko)/(49*t10^2)*t81*q+(t10),(-162*t20*ko)/(49*t10^3)*t81*q+(t20),(-66*t20*ko)/(7*t10^2)*t81*q+(t10*t20),16/(147*t10^2)*t81*q+(-t10)/(36*ko),45/(49*t10)*t81*q+(-t10^2)/(12*ko),(3888*t10^3*ko)/49*t81*q,1/(1512*t10*t20*ko)*t81*q+(-t10^2)/(1296*t20*ko^2),t81*q+(-t10^3)/(36*ko);
list vecfield=dt1,dt2,dt3,dt4,dt5,dt6,dt7,dt8;
list denomv=dis,dis,dis,dis,dis,dis,dis,dis;
intvec upto=1,1,1,1,1,1,1,1;intvec whichpow;
int iter=20;
int n;
for (n=2; n<=iter;n=n+1){upto=n,n,n,n,n,n,n,n; whichpow=upto;pose=qexpansion(vecfield,denomv,pose,upto,upto,a); n;}
1/2*pose[5]+1/144;

A300200 Coefficients of non-constant terms of a Calabi-Yau modular form attached to 4-dimensional Dwork family.

Original entry on oeis.org

7, 32859, 414746092, 7395891627375, 157811370338782458, 3761184845284146266940, 96638294064005241184266264, 2621887105259172896228800649079, 74130802295910304117947807929139019, 2164904215453533741015504646568354733618

Offset: 1

Younes Nikdelan, Mar 22 2018

nonn

The 8-tuple (1/36 + 20*A300194, -1 +216*A300195, -1/36 + 14*A300196, -1/6 + 24*A300197, -1/72 + 2*A300198, -1/46656 * A300199, 1/36 - 2*A300200,  -1/7776 + 7/18 * A300201)  gives a solution of the modular vector field R = Sum_{i=1..8} R_i d/dt_i on the enhanced moduli space arising from 4-dimensional Dwork family, where d/dt_i's give the standard basis of the tangent space in the chart (t_1,t_2,...,t_8) and
R_1 = -t_1*t_2+t_3;
R_2 = (-t_1^6*t_2^2+1/36*t_3^2*t_4*t_8+t_2^2*t_6)/(t_1^6-t_6);
R_3 = (-3*t_1^6*t_2*t_3+1/36*t_3^2*t_5*t_8+3*t_2*t_3*t_6)/(t_1^6-t_6);
R_4 = (-t_1^6*t_2*t_4-1/36*t_3^2*t_7*t_8+t_2*t_4*t_6)/(t_1^6-t_6);
R_5 = (-2*t_1^6*t_3*t_4-4*t_1^6*t_2*t_5+5*t_1^4*t_3*t_8+1/36*t_3*t_5^2*t_8+ 2*t_3*t_4*t_6+4*t_2*t_5*t_6)/(2*(t_1^6-t_6));
R_6 = -6*t_2*t_6;
R_7 = -18*t_1^2+1/2*t_4^2;
R_8 = (-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8)/(t_1^6-t_6);
For more details see the Movasati & Nikdelan link Section 8.3.

H. Movasati, Y. Nikdelan, Gauss-Manin Connection in Disguise: Dwork Family, arXiv:1603.09411 [math.AG], 2016-2017. See Table 2, (-1/2)*t_7.
H. Movasati, Foliation.lib.

Cf. A300194, A300195, A300196, A300197, A300198, A300199, A300201.

// This program has to be compiled in SINGULAR. By changing "int iter" you can
// calculate more coefficients. Note that this program is using a library calling
// "foliation.lib" written by H. Movasati, which is available in the link given in
// LINKS section as Foliation.lib.
LIB "linalg.lib"; LIB "foliation.lib";
ring r=0, (t_1,t_2,t_3,t_4,t_5,t_6,t_7,t_8,q),dp;
int pm=1;number t10=1/36;number ko=1/216;number c4=ko^2;number t20=-1;number t81=49/18;number a=-6*t20;
poly dis=t_1^6-t_6;
poly dt1=dis*(-t_1*t_2+t_3);
poly dt2=(1296*c4*t_3^2*t_4*t_8-t_1^6*t_2^2+t_2^2*t_6);
poly dt3=(1296*c4*t_3^2*t_5*t_8-3*t_1^6*t_2*t_3+3*t_2*t_3*t_6);
poly dt4=(-1296*c4*t_3^2*t_7*t_8-t_1^6*t_2*t_4+t_2*t_4*t_6);
poly dt5=(1296*c4*t_3*t_5^2*t_8-4*t_1^6*t_2*t_5-2*t_1^6*t_3*t_4+5*t_1^4*t_3*t_8+4*t_2*t_5*t_6+2*t_3*t_4*t_6)/(2);
poly dt6=dis*(-6*t_2*t_6);
poly dt7=dis*((1296*c4*t_4^2-t_1^2)/(2592*c4));
poly dt8=(-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8);
list pose;
pose=(60*ko)/(49*t10^2)*t81*q+(t10),(-162*t20*ko)/(49*t10^3)*t81*q+(t20),(-66*t20*ko)/(7*t10^2)*t81*q+(t10*t20),16/(147*t10^2)*t81*q+(-t10)/(36*ko),45/(49*t10)*t81*q+(-t10^2)/(12*ko),(3888*t10^3*ko)/49*t81*q,1/(1512*t10*t20*ko)*t81*q+(-t10^2)/(1296*t20*ko^2),t81*q+(-t10^3)/(36*ko);
list vecfield=dt1,dt2,dt3,dt4,dt5,dt6,dt7,dt8;
list denomv=dis,dis,dis,dis,dis,dis,dis,dis;
intvec upto=1,1,1,1,1,1,1,1;intvec whichpow;
int iter=20;
int n;
for (n=2; n<=iter;n=n+1){upto=n,n,n,n,n,n,n,n; whichpow=upto;pose=qexpansion(vecfield,denomv,pose,upto,upto,a); n;}
-1/2*pose[7];

A300201 Coefficients of non-constant terms of a Calabi-Yau modular form attached to the 4-dimensional Dwork family.

Original entry on oeis.org

7, 54855, 1034706148, 24546181658391, 653902684588247058, 18687787944102314534628, 559904113526412529297895976, 17354691863853902532743058359703, 551873714646783457391913160851776659, 17903944334292612333529257451439091620754

Offset: 1

Younes Nikdelan, Mar 28 2018

nonn

The 8-tuple (1/36 + 20*A300194, -1 + 216*A300195, -1/36 + 14*A300196, -1/6 + 24*A300197, -1/72 + 2*A300198, -1/46656 * A300199, 1/36 - 2*A300200,  -1/7776 + 7/18 * A300201) gives a solution to the modular vector field R = Sum_{i=1..8} R_i d/dt_i on the enhanced moduli space arising from the 4-dimensional Dwork family, where d/dt_i's give the standard basis of the tangent space in the chart (t_1,t_2,...,t_8) and
R_1 = -t_1*t_2+t_3;
R_2 = (-t_1^6*t_2^2+1/36*t_3^2*t_4*t_8+t_2^2*t_6)/(t_1^6-t_6);
R_3 = (-3*t_1^6*t_2*t_3+1/36*t_3^2*t_5*t_8+3*t_2*t_3*t_6)/(t_1^6-t_6);
R_4 = (-t_1^6*t_2*t_4-1/36*t_3^2*t_7*t_8+t_2*t_4*t_6)/(t_1^6-t_6);
R_5 = (-2*t_1^6*t_3*t_4-4*t_1^6*t_2*t_5+5*t_1^4*t_3*t_8+1/36*t_3*t_5^2*t_8+ 2*t_3*t_4*t_6+4*t_2*t_5*t_6)/(2*(t_1^6-t_6));
R_6 = -6*t_2*t_6;
R_7 = -18*t_1^2+1/2*t_4^2;
R_8 = (-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8)/(t_1^6-t_6);
For more details see Section 8.3 of the Movasati & Nikdelan link.

H. Movasati, Foliation.lib.
H. Movasati, Y. Nikdelan, Gauss-Manin Connection in Disguise: Dwork Family, arXiv:1603.09411 [math.AG], 2016-2017. See Table 2, (18/7)*t_8.

Cf. A300194, A300195, A300196, A300197, A300198, A300199, A300200.

// This program has to be compiled in SINGULAR. By changing "int iter" you can
// calculate more coefficients. Note that this program is using a library calling
// "foliation.lib" written by H. Movasati, which is available in the link given in
// LINKS section as Foliation.lib.
LIB "linalg.lib"; LIB "foliation.lib";
ring r=0, (t_1,t_2,t_3,t_4,t_5,t_6,t_7,t_8,q),dp;
int pm=1;number t10=1/36;number ko=1/216;number c4=ko^2;number t20=-1;number t81=49/18;number a=-6*t20;
poly dis=t_1^6-t_6;
poly dt1=dis*(-t_1*t_2+t_3);
poly dt2=(1296*c4*t_3^2*t_4*t_8-t_1^6*t_2^2+t_2^2*t_6);
poly dt3=(1296*c4*t_3^2*t_5*t_8-3*t_1^6*t_2*t_3+3*t_2*t_3*t_6);
poly dt4=(-1296*c4*t_3^2*t_7*t_8-t_1^6*t_2*t_4+t_2*t_4*t_6);
poly dt5=(1296*c4*t_3*t_5^2*t_8-4*t_1^6*t_2*t_5-2*t_1^6*t_3*t_4+5*t_1^4*t_3*t_8+4*t_2*t_5*t_6+2*t_3*t_4*t_6)/(2);
poly dt6=dis*(-6*t_2*t_6);
poly dt7=dis*((1296*c4*t_4^2-t_1^2)/(2592*c4));
poly dt8=(-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8);
list pose;
pose=(60*ko)/(49*t10^2)*t81*q+(t10),(-162*t20*ko)/(49*t10^3)*t81*q+(t20),(-66*t20*ko)/(7*t10^2)*t81*q+(t10*t20),16/(147*t10^2)*t81*q+(-t10)/(36*ko),45/(49*t10)*t81*q+(-t10^2)/(12*ko),(3888*t10^3*ko)/49*t81*q,1/(1512*t10*t20*ko)*t81*q+(-t10^2)/(1296*t20*ko^2),t81*q+(-t10^3)/(36*ko);
list vecfield=dt1,dt2,dt3,dt4,dt5,dt6,dt7,dt8;
list denomv=dis,dis,dis,dis,dis,dis,dis,dis;
intvec upto=1,1,1,1,1,1,1,1;intvec whichpow;
int iter=20;
int n;
for (n=2; n<=iter;n=n+1){upto=n,n,n,n,n,n,n,n; whichpow=upto;pose=qexpansion(vecfield,denomv,pose,upto,upto,a); n;}
18/7*pose[8]+1/3024;

A076909 Coefficients of 4-point function in dimension 4.

Original entry on oeis.org

6, 120960, 4136832000, 148146924602880, 5420219848911544320, 200623934537137119778560, 7478994517395643259712737280, 280135301818357004749298146851840, 10528167289356385699173014219946393600, 396658819202496234945300681212382224722560, 14972930462574202465673643937107499992165427200

Offset: 0

N. J. A. Sloane, Nov 28 2002

nonn

David R. Morrison, Mathematical Aspects of Mirror Symmetry, arXiv:alg-geom/9609021, 1996; in Complex Algebraic Geometry (J. Kollár, ed.), IAS/Park City Math. Series, vol. 3, 1997, pp. 265-340
H. Movasati, Foliation.lib.
H. Movasati, Y. Nikdelan, Gauss-Manin Connection in Disguise: Dwork Family, arXiv:1603.09411 [math.AG], 2016-2017. See (1/6)Y_1^2(q) in Section 8.3.

// This program has to be compiled in SINGULAR. By changing "int iter" you can
// calculate more coefficients. Note that this program is using a library calling
// "foliation.lib" written by H. Movasati, which is available in the link given in
// LINKS section as Foliation.lib.
LIB "linalg.lib"; LIB "foliation.lib";
ring r=0, (t_1,t_2,t_3,t_4,t_5,t_6,t_7,t_8,q),dp;
int pm=1;number t10=1/36;number ko=1/216;number c4=ko^2;number t20=-1;number t81=49/18;number a=-6*t20;
poly dis=t_1^6-t_6;
poly dt1=dis*(-t_1*t_2+t_3);
poly dt2=(1296*c4*t_3^2*t_4*t_8-t_1^6*t_2^2+t_2^2*t_6);
poly dt3=(1296*c4*t_3^2*t_5*t_8-3*t_1^6*t_2*t_3+3*t_2*t_3*t_6);
poly dt4=(-1296*c4*t_3^2*t_7*t_8-t_1^6*t_2*t_4+t_2*t_4*t_6);
poly dt5=(1296*c4*t_3*t_5^2*t_8-4*t_1^6*t_2*t_5-2*t_1^6*t_3*t_4+ 5*t_1^4*t_3*t_8+4*t_2*t_5*t_6+2*t_3*t_4*t_6)/(2);
poly dt6=dis*(-6*t_2*t_6);
poly dt7=dis*((1296*c4*t_4^2-t_1^2)/(2592*c4));
poly dt8=(-3*t_1^6*t_2*t_8+3*t_1^5*t_3*t_8+3*t_2*t_6*t_8);
list pose;
pose=(60*ko)/(49*t10^2)*t81*q+(t10),(-162*t20*ko)/(49*t10^3)*t81*q+(t20),(-66*t20*ko)/(7*t10^2)*t81*q+(t10*t20),16/(147*t10^2)*t81*q+(-t10)/(36*ko),45/(49*t10)*t81*q+(-t10^2)/(12*ko),(3888*t10^3*ko)/49*t81*q,1/(1512*t10*t20*ko)*t81*q+(-t10^2)/(1296*t20*ko^2),t81*q+(-t10^3)/(36*ko);
list vecfield=dt1,dt2,dt3,dt4,dt5,dt6,dt7,dt8;
list denomv=dis,dis,dis,dis,dis,dis,dis,dis;
intvec upto=1,1,1,1,1,1,1,1;intvec whichpow;
int iter=10;
int n;
for (n=2; n<=iter;n=n+1){upto=n,n,n,n,n,n,n,n; whichpow=upto;pose=qexpansion(vecfield,denomv,pose,upto,upto,a); n;}
poly y=1/216*pose[3]^4*OneOver(pose[1]^6-pose[6],std(ideal(q^(iter+1))),iter+1);
reduce(y,std(ideal(q^(iter+1))));
/* Younes Nikdelan, Mar 28 2018 */

G.f.: ((-1/36 + 14*A300196)^4)/(216((1/36 + 20*A300194)^6+1/46656 * A300199)), where the sequence numbers stand for the generating functions of the respective sequences. This is from equation (7.13) of the Movasati & Nikdelan link. - Younes Nikdelan, Mar 28 2018

a(8)-a(10) from Younes Nikdelan, Feb 28 2018

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A300196 Coefficients of non-constant terms of a Calabi-Yau modular form attached to 4-dimensional Dwork family.

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A300199 Coefficients of non-constant terms of a Calabi-Yau modular form attached to 4-dimensional Dwork family.

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A300195 Coefficients of non-constant terms of a Calabi-Yau modular form attached to 4-dimensional Dwork family.

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A300197 Coefficients of non-constant terms of a Calabi-Yau modular form attached to 4-dimensional Dwork family.

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A300198 Coefficients of non-constant terms of a Calabi-Yau modular form attached to 4-dimensional Dwork family.

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A300200 Coefficients of non-constant terms of a Calabi-Yau modular form attached to 4-dimensional Dwork family.

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A300201 Coefficients of non-constant terms of a Calabi-Yau modular form attached to the 4-dimensional Dwork family.

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A076909 Coefficients of 4-point function in dimension 4.

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