A289639 - OEIS

%I #25 Jul 11 2017 08:46:33

%S 264,340560,141251616,85062410400,43377095394864,23729517350865216,

%T 12591243615814264896,6769208775901467246912,

%U 3618692733697667332476264,1939201752717876551124987360,1038098212042387655796115897440

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

%H Seiichi Manyama, <a href="/A289639/b289639.txt">Table of n, a(n) for n = 1..366</a>

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

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

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

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

%F a(n) ~ exp(2*Pi*n). - _Vaclav Kotesovec_, Jul 09 2017

%t 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 *)

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

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

%K nonn

%O 1,1

%A _Seiichi Manyama_, Jul 09 2017