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Coefficients in q-expansion of E_4*E_6^2, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973.
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%I #12 Feb 26 2018 17:23:33

%S 1,-768,-19008,67329024,4834170816,137655866880,2122110676224,

%T 21418943158272,158760815970240,928988742914304,4512155542392960,

%U 18847838706545664,69519052583699712,230952254655327744,701948326302761472,1975789128222443520

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

%H Seiichi Manyama, <a href="/A282287/b282287.txt">Table of n, a(n) for n = 0..1000</a>

%t terms = 16;

%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]^2 + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)

%Y 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).

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

%K sign

%O 0,2

%A _Seiichi Manyama_, Feb 11 2017