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

%I #14 Feb 27 2018 04:57:31

%S 1,-1776,975888,-66529344,-79516693488,9511628122080,2031621786790848,

%T 134911299030780288,4962883791154433040,119289719378991436368,

%U 2051366007318600561120,26893975935849646148928,281804567385216854182848

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

%H Seiichi Manyama, <a href="/A282404/b282404.txt">Table of n, a(n) for n = 0..1000</a>

%t terms = 13;

%t E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];

%t E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];

%t E4[x]*E6[x]^4 + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 27 2018 *)

%Y Cf. A013974 (E_4*E_6 = E_10), A282287 (E_4*E_6^2), A282328 (E_4*E_6^3), this sequence (E_4*E_6^4).

%K sign

%O 0,2

%A _Seiichi Manyama_, Feb 14 2017