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Coefficients in q-expansion of E_2^2*E_4, where E_2 and E_4 are respectively the Eisenstein series A006352 and A004009.
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%I #18 Feb 26 2018 17:23:10

%S 1,192,-8928,9984,1420896,11433600,53760384,187233792,533725920,

%T 1327018944,2953851840,6060858624,11611915392,21030301824,36387585792,

%U 60357358080,97020376032,150755202432,229107724704,338493223680,492378465600,698632525824,980953593984

%N Coefficients in q-expansion of E_2^2*E_4, where E_2 and E_4 are respectively the Eisenstein series A006352 and A004009.

%H Seiichi Manyama, <a href="/A282208/b282208.txt">Table of n, a(n) for n = 0..1000</a>

%t terms = 23;

%t E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];

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

%t E2[x]^2*E4[x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)

%Y Cf. A006352 (E_2), A004009 (E_4), A281374 (E_2^2), A282019 (E_2*E_4), A008410 (E_4^2 = E_8), A282018 (E_2^3), this sequence (E_2^2*E_4), A282101 (E_2*E_4^2), A008411 (E_4^3).

%K sign

%O 0,2

%A _Seiichi Manyama_, Feb 09 2017