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.

1, 216, -3672, -62496, -322488, -1121904, -2969568, -6737472, -13678200, -24978312, -43826832, -70620768, -112325472, -166558896, -248342976, -346320576, -491604984, -655461072, -897864696, -1154109600, -1532856528, -1921344768, -2488726944, -3042415296, -3876616800, -4639932504

Offset: 0

Author

N. J. A. Sloane, Feb 05 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A004009, A006352.

Programs

Maple

with(numtheory); M:=100;
E := proc(k) local n, t1; global M;
t1 := 1-(2*k/bernoulli(k))*add(sigma[k-1](n)*q^n, n=1..M+1);
series(t1, q, M+1); end;
e2:=E(2); e4:=E(4); e6:=E(6);
series(e2*e4,q,M+1);
seriestolist(%);

Mathematica

terms = 26;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E2[x]*E4[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 23 2018 *)