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A282020 Coefficients in q-expansion of (E_2^3 - E_2*E_4)/288, where E_2 and E_4 are the Eisenstein series shown in A006352 and A004009, respectively.

%I A282020 #17 Feb 27 2018 09:36:04
%S A282020 0,-1,18,204,788,2250,4968,9688,17640,27747,45900,64548,98448,128674,
%T A282020 188496,232200,326864,386478,537354,608380,819000,926688,1214136,
%U A282020 1323144,1758240,1852625,2401308,2584440,3252256,3385170,4374000,4433248,5604768,5840208,7143876,7232400,9239364,9058858
%N A282020 Coefficients in q-expansion of (E_2^3 - E_2*E_4)/288, where E_2 and E_4 are the Eisenstein series shown in A006352 and A004009, respectively.
%H A282020 Seiichi Manyama, <a href="/A282020/b282020.txt">Table of n, a(n) for n = 0..1000</a>
%F A282020 a(n) = (A282018(n) - A282019(n))/288. - _Seiichi Manyama_, Feb 06 2017
%p A282020 with(numtheory); M:=100;
%p A282020 E := proc(k) local n, t1; global M;
%p A282020 t1 := 1-(2*k/bernoulli(k))*add(sigma[k-1](n)*q^n, n=1..M+1);
%p A282020 series(t1, q, M+1); end;
%p A282020 e2:=E(2); e4:=E(4); e6:=E(6);
%p A282020 series((e2^3-e2*e4)/288,q,M+1);
%p A282020 seriestolist(%);
%t A282020 terms = 38;
%t A282020 E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
%t A282020 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms + 1}];
%t A282020 (E2[x]^3 - E2[x]*E4[x])/288 + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 27 2018 *)
%Y A282020 Cf. A282018 (E_2^3), A282019 (E_2*E_4).
%K A282020 sign
%O A282020 0,3
%A A282020 _N. J. A. Sloane_, Feb 06 2017