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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.
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%I #17 Feb 27 2018 09:36:04

%S 0,-1,18,204,788,2250,4968,9688,17640,27747,45900,64548,98448,128674,

%T 188496,232200,326864,386478,537354,608380,819000,926688,1214136,

%U 1323144,1758240,1852625,2401308,2584440,3252256,3385170,4374000,4433248,5604768,5840208,7143876,7232400,9239364,9058858

%N 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 Seiichi Manyama, <a href="/A282020/b282020.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = (A282018(n) - A282019(n))/288. - _Seiichi Manyama_, Feb 06 2017

%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((e2^3-e2*e4)/288,q,M+1);

%p seriestolist(%);

%t terms = 38;

%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 + 1}];

%t (E2[x]^3 - E2[x]*E4[x])/288 + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 27 2018 *)

%Y Cf. A282018 (E_2^3), A282019 (E_2*E_4).

%K sign

%O 0,3

%A _N. J. A. Sloane_, Feb 06 2017