A282332 Coefficients in q-expansion of E_4^3*E_6^2, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.

1, -288, -325728, 11700864, 35176468896, 6601058210880, 438061091013504, 15173572442740992, 327251435243536800, 4913611331706352224, 55439979246339307200, 496425441863436557184, 3672747479405396310912, 23148319784349233726784

Offset: 0

Author

Seiichi Manyama, Feb 12 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Eisenstein Series.

Crossrefs

Cf. A280869 (E_6^2), A282287 (E_4*E_6^2), A282292 (E_4^2*E_6^2 = E_10^2), this sequence (E_4^3*E_6^2).

Programs

Mathematica

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]^3*E6[x]^2 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)