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A282019 Coefficients in q-expansion of E_2*E_4, where E_2 and E_4 are the Eisenstein series shown in A006352 and A004009, respectively.

%I A282019 #11 Feb 23 2018 03:40:36
%S A282019 1,216,-3672,-62496,-322488,-1121904,-2969568,-6737472,-13678200,
%T A282019 -24978312,-43826832,-70620768,-112325472,-166558896,-248342976,
%U A282019 -346320576,-491604984,-655461072,-897864696,-1154109600,-1532856528,-1921344768,-2488726944,-3042415296,-3876616800,-4639932504
%N A282019 Coefficients in q-expansion of E_2*E_4, where E_2 and E_4 are the Eisenstein series shown in A006352 and A004009, respectively.
%H A282019 Seiichi Manyama, <a href="/A282019/b282019.txt">Table of n, a(n) for n = 0..1000</a>
%p A282019 with(numtheory); M:=100;
%p A282019 E := proc(k) local n, t1; global M;
%p A282019 t1 := 1-(2*k/bernoulli(k))*add(sigma[k-1](n)*q^n, n=1..M+1);
%p A282019 series(t1, q, M+1); end;
%p A282019 e2:=E(2); e4:=E(4); e6:=E(6);
%p A282019 series(e2*e4,q,M+1);
%p A282019 seriestolist(%);
%t A282019 terms = 26;
%t A282019 E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
%t A282019 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A282019 E2[x]*E4[x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 23 2018 *)
%Y A282019 Cf. A004009, A006352.
%K A282019 sign
%O A282019 0,2
%A A282019 _N. J. A. Sloane_, Feb 05 2017