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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.
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%I #12 Feb 27 2018 07:09:13

%S 1,-1536,551808,163854336,-93387735168,-9709554816000,

%T 4142226444876288,642510156233453568,41792421673548259200,

%U 1615606968766288470528,42343208407470359036160,812663841518551604717568,12060089370317565140003328

%N 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.

%H Seiichi Manyama, <a href="/A282543/b282543.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]^2*E6[x]^4 + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 27 2018 *)

%Y 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).

%K sign

%O 0,2

%A _Seiichi Manyama_, Feb 17 2017