A289640 Coefficients in expansion of -q*E'_14/E_14 where E_14 is the Eisenstein Series (A058550).

24, 393840, 128962656, 87898218720, 42722691563664, 23880530579622336, 12556395110261366976, 6777250576938845733312, 3616836970791932655993144, 1939629997080836352904793760, 1037999388408269242271021494560

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), A289639 (k=10), this sequence (k=14).

Cf. A006352 (E_2), A058550 (E_14), A287964, A289029.

Programs

Mathematica

nmax = 20; Rest[CoefficientList[Series[24*x*Sum[k*DivisorSigma[13, k]*x^(k-1), {k, 1, nmax}]/(1 - 24*Sum[DivisorSigma[13, k]*x^k, {k, 1, nmax}]), {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jul 09 2017 *)

Formula

a(n) = Sum_{d|n} d * A289029(d).

a(n) = 2*A288261(n)/3 + A288840(n)/2 + 28*A000203(n).

a(n) = -Sum_{k=1..n-1} A058550(k)*a(n-k) - A058550(n)*n.

G.f.: 2/3 * E_6/E_4 + 1/2 * E_8/E_6 - 7/6 * E_2.

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