A282543 Coefficients in q-expansion of E_4^2*E_6^4, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.

1, -1536, 551808, 163854336, -93387735168, -9709554816000, 4142226444876288, 642510156233453568, 41792421673548259200, 1615606968766288470528, 42343208407470359036160, 812663841518551604717568, 12060089370317565140003328

Offset: 0

Author

Seiichi Manyama, Feb 17 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), A282357 (E_4^2*E_6^3), this sequence (E_4^2*E_6^4).

Programs

Mathematica

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]^2*E6[x]^4 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)