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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.
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%I #11 Feb 23 2018 03:40:36

%S 1,216,-3672,-62496,-322488,-1121904,-2969568,-6737472,-13678200,

%T -24978312,-43826832,-70620768,-112325472,-166558896,-248342976,

%U -346320576,-491604984,-655461072,-897864696,-1154109600,-1532856528,-1921344768,-2488726944,-3042415296,-3876616800,-4639932504

%N 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 Seiichi Manyama, <a href="/A282019/b282019.txt">Table of n, a(n) for n = 0..1000</a>

%p with(numtheory); M:=100;

%p E := proc(k) local n, t1; global M;

%p t1 := 1-(2*k/bernoulli(k))*add(sigma[k-1](n)*q^n, n=1..M+1);

%p series(t1, q, M+1); end;

%p e2:=E(2); e4:=E(4); e6:=E(6);

%p series(e2*e4,q,M+1);

%p seriestolist(%);

%t terms = 26;

%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]*E4[x] + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 23 2018 *)

%Y Cf. A004009, A006352.

%K sign

%O 0,2

%A _N. J. A. Sloane_, Feb 05 2017