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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.
3

%I #12 Feb 27 2018 02:58:01

%S 1,-1032,48312,171162336,-6444771144,-10105554483504,

%T -1037089473751584,-48959817978105408,-1378102838778701640,

%U -26186640301645703016,-364779940958775418032,-3952291567255306906464,-34798629548716507265568,-257403564989318828310384

%N 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.

%H Seiichi Manyama, <a href="/A282357/b282357.txt">Table of n, a(n) for n = 0..1000</a>

%t terms = 14;

%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]^3 + 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), this sequence (E_4^2*E_6^3).

%K sign

%O 0,2

%A _Seiichi Manyama_, Feb 13 2017