A289637 Coefficients in expansion of -q*E'_6/E_6 where E_6 is the Eisenstein Series (A013973).

504, 287280, 153540576, 82226602080, 44031499226064, 23578504122108096, 12626092121367162816, 6761166974864088760512, 3620548496603402008959384, 1938773508354916749345180960, 1038197035676506069321210300320

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), this sequence (k=6), A289638 (k=8), A289639 (k=10), A289640 (k=14).

Cf. A000706, A006352 (E_2), A013973 (E_6), A145095, A288851.

Programs

Mathematica

nmax = 20; Rest[CoefficientList[Series[504*x*Sum[k*DivisorSigma[5, k]*x^(k-1), {k, 1, nmax}]/(1 - 504*Sum[DivisorSigma[5, k]*x^k, {k, 1, nmax}]), {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jul 09 2017 *)

Formula

a(n) = Sum_{d|n} d * A288851(d).

a(n) = A288840(n)/2 + 12*A000203(n).

a(n) = -Sum_{k=1..n-1} A013973(k)*a(n-k) - A013973(n)*n.

G.f.: 1/2 * E_8/E_6 - 1/2 * E_2.

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