A282357 Coefficients in q-expansion of E_4^2*E_6^3, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.

1, -1032, 48312, 171162336, -6444771144, -10105554483504, -1037089473751584, -48959817978105408, -1378102838778701640, -26186640301645703016, -364779940958775418032, -3952291567255306906464, -34798629548716507265568, -257403564989318828310384

Offset: 0

Author

Seiichi Manyama, Feb 13 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A008410 (E_4^2 = E_8), A058550 (E_4^2*E_6 = E_14), A282292 (E_4^2*E_6^2 = E_10^2), this sequence (E_4^2*E_6^3).

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