A289639 Coefficients in expansion of -q*E'_10/E_10 where E_10 is the Eisenstein Series (A013974).

264, 340560, 141251616, 85062410400, 43377095394864, 23729517350865216, 12591243615814264896, 6769208775901467246912, 3618692733697667332476264, 1939201752717876551124987360, 1038098212042387655796115897440

Offset: 1

Author

Seiichi Manyama, Jul 09 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..366

Crossrefs

-q*E'_k/E_k: A289635 (k=2), A289636 (k=4), A289637 (k=6), A289638 (k=8), this sequence (k=10), A289640 (k=14).

Cf. A006352 (E_2), A013974 (E_10), A285836, A289024.

Programs

Mathematica

nmax = 20; Rest[CoefficientList[Series[264*x*Sum[k*DivisorSigma[9, k]*x^(k-1), {k, 1, nmax}]/(1 - 264*Sum[DivisorSigma[9, k]*x^k, {k, 1, nmax}]), {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jul 09 2017 *)

Formula

a(n) = Sum_{d|n} d * A289024(d).

a(n) = A288261(n)/3 + A288840(n)/2 + 20*A000203(n).

a(n) = -Sum_{k=1..n-1} A013974(k)*a(n-k) - A013974(n)*n.

G.f.: 1/3 * E_6/E_4 + 1/2 * E_8/E_6 - 5/6 * E_2.

a(n) ~ exp(2*Pi*n). - Vaclav Kotesovec, Jul 09 2017