A341243 -id:A341243 - cp's OEIS frontend

A341245 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^6.

1, 0, 6, 6, 21, 36, 71, 132, 222, 392, 633, 1038, 1629, 2544, 3885, 5842, 8691, 12738, 18494, 26520, 37722, 53132, 74235, 102882, 141579, 193506, 262713, 354552, 475749, 634932, 842922, 1113630, 1464450, 1917254, 2499330, 3244998, 4196966, 5408004, 6943632, 8884996

Offset: 6

Ilya Gutkovskiy, Feb 07 2021

nonn

Cf. A000700, A001484, A022601, A112150, A327384, A338463, A341225, A341241, A341243, A341244, A341246, A341247, A341251.

g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]
      [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
    end:
b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, g(n)),
      (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
    end:
a:= n-> b(n, 6):
seq(a(n), n=6..45);  # Alois P. Heinz, Feb 07 2021

nmax = 45; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^6, {x, 0, nmax}], x] // Drop[#, 6] &

G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^6.

A341246 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^7.

Original entry on oeis.org

1, 0, 7, 7, 28, 49, 105, 203, 364, 672, 1141, 1960, 3220, 5250, 8359, 13104, 20272, 30877, 46522, 69195, 101941, 148604, 214697, 307475, 436849, 615965, 862246, 1199009, 1656642, 2275231, 3106824, 4219502, 5701066, 7664923, 10256771, 13663574, 18123924, 23941190

Offset: 7

Ilya Gutkovskiy, Feb 07 2021

nonn

Cf. A000700, A001485, A022602, A327385, A338463, A341226, A341241, A341243, A341244, A341245, A341247, A341251.

g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]
      [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
    end:
b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, g(n)),
      (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
    end:
a:= n-> b(n, 7):
seq(a(n), n=7..44);  # Alois P. Heinz, Feb 07 2021

nmax = 44; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &

G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^7.

A341247 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^8.

Original entry on oeis.org

1, 0, 8, 8, 36, 64, 148, 296, 562, 1080, 1920, 3440, 5890, 9992, 16532, 26920, 43175, 68144, 106260, 163472, 248824, 374504, 558212, 824208, 1206409, 1751360, 2522692, 3607456, 5122848, 7227392, 10132948, 14123000, 19573393, 26981768, 37003700, 50499952, 68595956

Offset: 8

Ilya Gutkovskiy, Feb 07 2021

nonn

Cf. A000700, A001486, A007259, A101127, A327386, A338463, A341227, A341241, A341243, A341244, A341245, A341246, A341251.

g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]
      [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
    end:
b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, g(n)),
      (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
    end:
a:= n-> b(n, 8):
seq(a(n), n=8..44);  # Alois P. Heinz, Feb 07 2021

nmax = 44; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^8, {x, 0, nmax}], x] // Drop[#, 8] &

G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^8.

A001483 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^5 in powers of x.

Original entry on oeis.org

1, -5, 10, -10, 0, 19, -35, 40, -25, -10, 45, -75, 80, -60, 15, 45, -85, 115, -115, 90, -21, -35, 95, -130, 135, -135, 70, -35, -65, 105, -146, 120, -150, 90, -65, -25, 90, -115, 150, -125, 130, -45, 80, 35, -5, 160, -110, 170, -85, 95, 25, 50, 0, -60, 95, -116, 120, -135

Offset: 5

N. J. A. Sloane

sign

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Alois P. Heinz, Table of n, a(n) for n = 5..10000
H. Gupta, On the coefficients of the powers of Dedekind's modular form, J. London Math. Soc., 39 (1964), 433-440.
H. Gupta, On the coefficients of the powers of Dedekind's modular form (annotated and scanned copy)

Cf. A001482, A001484 - A001488, A047638 - A047649, A047654, A047655, A341243.

m:=102;
R:=PowerSeriesRing(Integers(), m);
Coefficients(R!( ((&*[1-(-x)^j: j in [1..m+2]]) -1)^5 )); // G. C. Greubel, Sep 04 2023

g:= proc(n) option remember; `if`(n=0, 1, add(add([-d, d, -2*d, d]
      [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
    end:
b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0, g(n)),
      (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
    end:
a:= n-> b(n, 5):
seq(a(n), n=5..62);  # Alois P. Heinz, Feb 07 2021

nmax = 62; CoefficientList[Series[(Product[(1 - (-x)^j), {j, 1, nmax}] - 1)^5, {x, 0, nmax}], x] // Drop[#, 5] & (* Ilya Gutkovskiy, Feb 07 2021 *)
Drop[CoefficientList[Series[(QPochhammer[-x] -1)^5, {x,0,102}], x], 5] (* G. C. Greubel, Sep 04 2023 *)

my(N=70,x='x+O('x^N)); Vec((eta(-x)-1)^5) \\ Joerg Arndt, Sep 04 2023

m=100; k=5;
def f(k,x): return (-1 + product( (1+x^j)*(1-x^(2*j))/(1+x^(2*j)) for j in range(1,m+2) ) )^k
def A001483_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( f(k,x) ).list()
a=A001483_list(m); a[k:] # G. C. Greubel, Sep 04 2023

a(n) = [x^n]( QPochhammer(-x) - 1 )^5. - G. C. Greubel, Sep 04 2023

Definition and offset edited by Ilya Gutkovskiy, Feb 07 2021

A001487 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^9 in powers of x.

Original entry on oeis.org

1, -9, 36, -84, 117, -54, -177, 540, -837, 755, -54, -1197, 2535, -3204, 2520, -246, -3150, 6426, -8106, 7011, -2844, -3549, 10359, -15120, 15804, -11403, 2574, 8610, -18972, 25425, -25824, 18954, -6165, -10080, 25101, -35262, 37799, -31374, 17379, 1929

Offset: 9

N. J. A. Sloane

sign

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Alois P. Heinz, Table of n, a(n) for n = 9..10000
H. Gupta, On the coefficients of the powers of Dedekind's modular form, J. London Math. Soc., 39 (1964), 433-440.
H. Gupta, On the coefficients of the powers of Dedekind's modular form (annotated and scanned copy)

Cf. A001482 - A001486, A001488, A047638 - A047649, A047654, A047655, A341243.

m:=102;
R:=PowerSeriesRing(Integers(), m);
Coefficients(R!( ((&*[1-(-x)^j: j in [1..m+2]]) -1)^9 )); // G. C. Greubel, Sep 04 2023

g:= proc(n) option remember; `if`(n=0, 1, add(add([-d, d, -2*d, d]
      [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
    end:
b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0, g(n)),
      (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
    end:
a:= n-> b(n, 9):
seq(a(n), n=9..48);  # Alois P. Heinz, Feb 07 2021

nmax=48; CoefficientList[Series[(Product[(1 - (-x)^j), {j,nmax}] -1)^9, {x,0,nmax}], x]//Drop[#,9] & (* Ilya Gutkovskiy, Feb 07 2021 *)
Drop[CoefficientList[Series[(QPochhammer[-x] -1)^9, {x,0,102}], x], 9] (* G. C. Greubel, Sep 04 2023 *)

my(N=55,x='x+O('x^N)); Vec((eta(-x)-1)^9) \\ Joerg Arndt, Sep 05 2023

from sage.modular.etaproducts import qexp_eta
m=100; k=9;
def f(k,x): return (-1 + qexp_eta(QQ[['q']], m+2).subs(q=-x) )^k
def A001487_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( f(k,x) ).list()
a=A001487_list(m); a[k:] # G. C. Greubel, Sep 04 2023

a(n) = [x^n]( QPochhammer(-x) - 1 )^9. - G. C. Greubel, Sep 04 2023

Definition and offset edited by Ilya Gutkovskiy, Feb 07 2021

A001484 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^6 in powers of x.

Original entry on oeis.org

1, -6, 15, -20, 9, 24, -65, 90, -75, 6, 90, -180, 220, -180, 66, 110, -264, 360, -365, 264, -66, -178, 375, -510, 496, -414, 180, 60, -330, 570, -622, 582, -390, 220, 96, -300, 621, -630, 705, -492, 300, 0, -235, 420, -570, 594, -735, 420, -420, -120, 219, -586, 360

Offset: 6

N. J. A. Sloane

sign

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Robert Israel, Table of n, a(n) for n = 6..10000
H. Gupta, On the coefficients of the powers of Dedekind's modular form, J. London Math. Soc., 39 (1964), 433-440.
H. Gupta, On the coefficients of the powers of Dedekind's modular form (annotated and scanned copy)

Cf. A001482, A001483, A001485 - A001488, A047638 - A047649, A047654, A047655, A341243.

m:=102;
R:=PowerSeriesRing(Integers(), m);
Coefficients(R!( ((&*[1-(-x)^j: j in [1..m+2]]) -1)^6 )); // G. C. Greubel, Sep 04 2023

N:= 100:
S:= series((mul(1-(-x)^j,j=1..N)-1)^6,x,N+1):
seq(coeff(S,x,j),j=6..N); # Robert Israel, Feb 05 2019

Drop[CoefficientList[Series[(QPochhammer[-x] -1)^6, {x,0,102}], x], 6] (* G. C. Greubel, Sep 04 2023 *)

my(N=70,x='x+O('x^N)); Vec((eta(-x)-1)^6) \\ Joerg Arndt, Sep 04 2023

m=100; k=6;
def f(k,x): return (-1 + product( (1+x^j)*(1-x^(2*j))/(1+x^(2*j)) for j in range(1,m+2) ) )^k
def A001484_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( f(k,x) ).list()
a=A001484_list(m); a[k:] # G. C. Greubel, Sep 04 2023

a(n) = [x^n] ( QPochhammer(-x) - 1 )^6. - G. C. Greubel, Sep 04 2023

Edited by Robert Israel, Feb 05 2019

A001485 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^7 in powers of x.

Original entry on oeis.org

1, -7, 21, -35, 28, 21, -105, 181, -189, 77, 140, -385, 546, -511, 252, 203, -693, 1029, -1092, 798, -203, -581, 1281, -1708, 1687, -1232, 413, 602, -1485, 2233, -2366, 2009, -1099, 14, 1099, -2072, 2667, -2807, 2254, -1477, 0, 1057, -2346, 2744, -3017, 2457

Offset: 7

N. J. A. Sloane

sign

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Alois P. Heinz, Table of n, a(n) for n = 7..10000
H. Gupta, On the coefficients of the powers of Dedekind's modular form, J. London Math. Soc., 39 (1964), 433-440.
H. Gupta, On the coefficients of the powers of Dedekind's modular form (annotated and scanned copy)

Cf. A001482, A001483, A001484, A001486, A001487, A001488, A047638 - A047649, A047654, A047655, A341243.

m:=102;
R:=PowerSeriesRing(Integers(), m);
Coefficients(R!( ((&*[1-(-x)^j: j in [1..m+2]]) -1)^7 )); // G. C. Greubel, Sep 04 2023

g:= proc(n) option remember; `if`(n=0, 1, add(add([-d, d, -2*d, d]
      [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
    end:
b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0, g(n)),
      (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
    end:
a:= n-> b(n, 7):
seq(a(n), n=7..52);  # Alois P. Heinz, Feb 07 2021

nmax = 52; CoefficientList[Series[(Product[(1 - (-x)^j), {j, 1, nmax}] - 1)^7, {x, 0, nmax}], x] // Drop[#, 7] & (* Ilya Gutkovskiy, Feb 07 2021 *)
Drop[CoefficientList[Series[(QPochhammer[-x] -1)^7, {x,0,102}], x], 7] (* G. C. Greubel, Sep 04 2023 *)

my(N=70,x='x+O('x^N)); Vec((eta(-x)-1)^7) \\ Joerg Arndt, Sep 04 2023

m=100; k=7;
def f(k,x): return (-1 + product( (1+x^j)*(1-x^(2*j))/(1+x^(2*j)) for j in range(1,m+2) ) )^k
def A001485_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( f(k,x) ).list()
a=A001485_list(m); a[k:] # G. C. Greubel, Sep 04 2023

a(n) = [x^n] ( QPochhammer(-x) - 1 )^7. - G. C. Greubel, Sep 04 2023

Definition and offset edited by Ilya Gutkovskiy, Feb 07 2021

A001486 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^8 in powers of x.

Original entry on oeis.org

1, -8, 28, -56, 62, 0, -148, 328, -419, 280, 140, -728, 1232, -1336, 848, 224, -1582, 2688, -3072, 2408, -742, -1568, 3836, -5264, 5306, -3744, 924, 2576, -5686, 7792, -8092, 6272, -2751, -1848, 6008, -9296, 10556, -9800, 6692, -2240, -3206, 8168, -11524

Offset: 8

N. J. A. Sloane

sign

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Alois P. Heinz, Table of n, a(n) for n = 8..10000
H. Gupta, On the coefficients of the powers of Dedekind's modular form, J. London Math. Soc., 39 (1964), 433-440.
H. Gupta, On the coefficients of the powers of Dedekind's modular form (annotated and scanned copy)

Cf. A001482 - A001485, A001487, A001488, A047638 - A047649, A047654, A047655, A341243.

m:=102;
R:=PowerSeriesRing(Integers(), m);
Coefficients(R!( ((&*[1-(-x)^j: j in [1..m+2]]) -1)^8 )); // G. C. Greubel, Sep 04 2023

g:= proc(n) option remember; `if`(n=0, 1, add(add([-d, d, -2*d, d]
      [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
    end:
b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0, g(n)),
      (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
    end:
a:= n-> b(n, 8):
seq(a(n), n=8..50);  # Alois P. Heinz, Feb 07 2021

nmax=50; CoefficientList[Series[(Product[(1 -(-x)^j), {j,nmax}] -1)^8, {x,0,nmax}], x]//Drop[#,8] & (* Ilya Gutkovskiy, Feb 07 2021 *)
Drop[CoefficientList[Series[(QPochhammer[-x] -1)^8, {x,0,102}], x], 8] (* G. C. Greubel, Sep 04 2023 *)

my(N=55,x='x+O('x^N)); Vec((eta(-x)-1)^8) \\ Joerg Arndt, Sep 05 2023

from sage.modular.etaproducts import qexp_eta
m=100; k=8;
def f(k,x): return (-1 + qexp_eta(QQ[['q']], m+2).subs(q=-x) )^k
def A001486_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( f(k,x) ).list()
a=A001486_list(m); a[k:] # G. C. Greubel, Sep 04 2023

a(n) = [x^n]( QPochhammer(-x) - 1 )^8. - G. C. Greubel, Sep 04 2023

Definition and offset edited by Ilya Gutkovskiy, Feb 07 2021

A047645 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^20 in powers of x.

Original entry on oeis.org

1, -20, 190, -1140, 4825, -15124, 35320, -57760, 45220, 80560, -405954, 910460, -1289340, 852340, 1259530, -5357924, 10151510, -12048660, 5883350, 12186960, -40135713, 66244280, -69648870, 28191460, 66920755, -195366168, 300881530

Offset: 20

N. J. A. Sloane

sign

Alois P. Heinz, Table of n, a(n) for n = 20..10000
H. Gupta, On the coefficients of the powers of Dedekind's modular form (annotated and scanned copy)
H. Gupta, On the coefficients of the powers of Dedekind's modular form, J. London Math. Soc., 39 (1964), 433-440.

Cf. A001482 - A001488, A001490, A047638 - A047644, A047646 - A047649, A047654, A047655, A341243.

m:=80;
R:=PowerSeriesRing(Integers(), m);
Coefficients(R!( ((&*[1-(-x)^j: j in [1..m+2]]) -1)^(20) )); // G. C. Greubel, Sep 06 2023

g:= proc(n) option remember; `if`(n=0, 1, add(add([-d, d, -2*d, d]
      [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
    end:
b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0, g(n)),
      (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
    end:
a:= n-> b(n, 20):
seq(a(n), n=20..46);  # Alois P. Heinz, Feb 07 2021

nmax=46; CoefficientList[Series[(Product[(1-(-x)^j), {j,nmax}] -1)^20, {x,0,nmax}], x]//Drop[#, 20] & (* Ilya Gutkovskiy, Feb 07 2021 *)
With[{k=20}, Drop[CoefficientList[Series[(QPochhammer[-x] -1)^k, {x,0, 75}], x], k]] (* G. C. Greubel, Sep 06 2023 *)

my(N=44, x='x+O('x^N)); Vec((eta(-x)-1)^20) \\ Joerg Arndt, Sep 06 2023

from sage.modular.etaproducts import qexp_eta
m=75; k=20;
def f(k,x): return (-1 + qexp_eta(QQ[['q']], m+2).subs(q=-x) )^k
def A047645_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( f(k,x) ).list()
a=A047645_list(m); a[k:] # G. C. Greubel, Sep 06 2023

a(n) = [x^n]( QPochhammer(-x) - 1 )^20. - G. C. Greubel, Sep 06 2023

Definition and offset edited by Ilya Gutkovskiy, Feb 07 2021

A047648 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^23 in powers of x.

Original entry on oeis.org

1, -23, 253, -1771, 8832, -33143, 95611, -209231, 317009, -181401, -686642, 2828977, -6099278, 8422623, -4906406, -10919687, 41968146, -78977952, 93297545, -40351223, -117265247, 367581446, -606562624, 631382751, -207879980, -777907725, 2132043121

Offset: 23

N. J. A. Sloane

sign

Alois P. Heinz, Table of n, a(n) for n = 23..10000
H. Gupta, On the coefficients of the powers of Dedekind's modular form (annotated and scanned copy)
H. Gupta, On the coefficients of the powers of Dedekind's modular form, J. London Math. Soc., 39 (1964), 433-440.

Cf. A001482 - A001488, A001490, A047638 - A047647, A047649, A047654, A047655, A341243.

m:=75;
R:=PowerSeriesRing(Integers(), m);
Coefficients(R!( ((&*[1-(-x)^j: j in [1..m+2]]) -1)^(23) )); // G. C. Greubel, Sep 05 2023

g:= proc(n) option remember; `if`(n=0, 1, add(add([-d, d, -2*d, d]
      [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
    end:
b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0, g(n)),
      (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
    end:
a:= n-> b(n, 23):
seq(a(n), n=23..49);  # Alois P. Heinz, Feb 07 2021

nmax=49; CoefficientList[Series[(Product[(1-(-x)^j), {j,nmax}] -1)^23, {x,0,nmax}], x]//Drop[#, 23] & (* Ilya Gutkovskiy, Feb 07 2021 *)
With[{k=23}, Drop[CoefficientList[Series[(QPochhammer[-x] -1)^k, {x,0, 75}], x], k]] (* G. C. Greubel, Sep 05 2023 *)

my(N=44, x='x+O('x^N)); Vec((eta(-x)-1)^23) \\ Joerg Arndt, Sep 05 2023

from sage.modular.etaproducts import qexp_eta
m=75; k=23;
def f(k,x): return (-1 + qexp_eta(QQ[['q']], m+2).subs(q=-x) )^k
def A047648_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( f(k,x) ).list()
a=A047648_list(m); a[k:] # G. C. Greubel, Sep 05 2023

a(n) = [x^n]( QPochhammer(-x) - 1 )^23. - G. C. Greubel, Sep 05 2023

Definition and offset edited by Ilya Gutkovskiy, Feb 07 2021

cp's OEIS Frontend

A341245 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^6.

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A341246 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^7.

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A341247 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^8.

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A001483 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^5 in powers of x.

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A001487 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^9 in powers of x.

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A001484 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^6 in powers of x.

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Magma

Maple

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A001485 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^7 in powers of x.

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