A281374 Coefficients in q-expansion of E_2^2, where E_2 is the Eisenstein series shown in A006352.

1, -48, 432, 3264, 9456, 21600, 39744, 66432, 105840, 147984, 220320, 281664, 393792, 475104, 646272, 743040, 980592, 1091232, 1432944, 1536960, 1965600, 2118144, 2649024, 2761344, 3516480, 3557040, 4433184, 4594560, 5575296, 5603040, 6998400, 6864384, 8407152, 8494848, 10085472, 9918720, 12319152

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. A000203, A001158, 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(e2^2,q,M+1);
seriestolist(%);

Mathematica

terms = 37;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E2[x]^2 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 23 2018 *)
(* or *)
Join[{1}, Table[240*DivisorSigma[3, n] - 288*n*DivisorSigma[1, n], {n, 1, 50}]] (* Vaclav Kotesovec, Aug 02 2025 *)

Formula

For n>0, a(n) = 240*A001158(n) - 288*n*A000203(n). - Vaclav Kotesovec, Aug 02 2025