A282000
Coefficients in q-expansion of E_4^3*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.
Original entry on oeis.org
1, 216, -200232, -85500576, -11218984488, -499862636784, -11084671590048, -152346382155072, -1474691273530920, -10921720940625672, -65489246355989232, -331011680696545248, -1452954445366288032, -5665058572086302256, -19968589327695656256
Offset: 0
- G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 208.
-
terms = 15;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E4[x]^3*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
A282047
Coefficients in q-expansion of E_4^4*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.
Original entry on oeis.org
1, 456, -146232, -133082976, -32170154808, -3378441902544, -155862776255328, -3969266446940352, -65538944782146360, -777506848190979672, -7105808014591457232, -52584752452485047328, -326903300701760852832, -1755591608260377411216
Offset: 0
- G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 208.
-
terms = 14;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E4[x]^4*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
A282356
Eisenstein series E_26(q) (alternate convention E_13(q)), multiplied by 657931.
Original entry on oeis.org
657931, -24, -805306392, -20334926626656, -27021598569529368, -7152557373046875024, -682326933054044766048, -32185646871935157619392, -906694391732570450559000, -17229551704624797057112632, -240000007152557373852181392
Offset: 0
Cf.
A006352 (E_2),
A004009 (E_4),
A013973 (E_6),
A008410 (E_8),
A013974 (E_10),
A029828 (691*E_12),
A058550 (E_14),
A029829 (3617*E_16),
A279892 (43867*E_18),
A029830 (174611*E_20),
A279893 (77683*E_22),
A029831 (236364091*E_24), this sequence (657931*E_26).
-
terms = 11;
E26[x_] = 657931 - 24*Sum[k^25*x^k/(1 - x^k), {k, 1, terms}];
E26[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
A282382
Coefficients in q-expansion of E_4^6*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.
Original entry on oeis.org
1, 936, 134568, -173988576, -104617833048, -27210540914064, -3910401774129888, -322823174243838912, -15429983442476298840, -469709326015243815672, -9973673112569954220432, -158215072218253260221088, -1972939697011615168926432
Offset: 0
-
terms = 13;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E4[x]^6*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
Showing 1-4 of 4 results.