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A282102 Coefficients in q-expansion of E_2*E_4*E_6, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.

%I A282102 #26 Mar 08 2021 23:36:59
%S A282102 1,-288,-129168,-1927296,65152656,1535768640,15223408704,98001292032,
%T A282102 474055120080,1870878793824,6312358836000,18835985199744,
%U A282102 50831420617152,126257508465984,292348744636032,637474437331200,1319883180896592,2610964045674432,4963491913583664
%N A282102 Coefficients in q-expansion of E_2*E_4*E_6, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
%C A282102 The series expansion of the 12th root of the generating function gives A341801. - _Peter Bala_, Feb 23 2021
%H A282102 Seiichi Manyama, <a href="/A282102/b282102.txt">Table of n, a(n) for n = 0..1000</a>
%t A282102 terms = 19;
%t A282102 E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
%t A282102 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A282102 E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t A282102 E2[x]*E4[x]*E6[x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 23 2018 *)
%Y A282102 Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A013974 (E_10).
%Y A282102 Cf. A281374 (E_2^2), A282019 (E_2*E_4), A282096 (E_2*E_6), A282101 (E_2*E_8), this sequence (E_2*E_10), A341801.
%K A282102 sign
%O A282102 0,2
%A A282102 _Seiichi Manyama_, Feb 06 2017