A282287 Coefficients in q-expansion of E_4*E_6^2, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.

1, -768, -19008, 67329024, 4834170816, 137655866880, 2122110676224, 21418943158272, 158760815970240, 928988742914304, 4512155542392960, 18847838706545664, 69519052583699712, 230952254655327744, 701948326302761472, 1975789128222443520

Offset: 0

Author

Seiichi Manyama, Feb 11 2017

Keywords

• sign

Links

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

Crossrefs

Cf. A004009 (E_4), A013973 (E_6), A008411 (E_4^3), A058550 (E_4^2*E_6 = E_14), this sequence (E_4*E_6^2), A282253 (E_6^3).

Cf. A282102 (E_2*E_10), A058550 (E_4*E_10), this sequence (E_6*E_10).

Programs

Mathematica

terms = 16;
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]*E6[x]^2 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)