login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

G.f.: Sum_{k>=1} x^(2*k)/(1-x^(2*k)) * Product_{k>=1} (1+x^k)/(1-x^k).
4

%I #7 May 25 2018 18:58:40

%S 0,0,1,2,6,12,24,44,79,134,222,358,566,876,1334,2000,2960,4326,6253,

%T 8946,12680,17816,24832,34352,47192,64404,87354,117796,157976,210764,

%U 279812,369744,486413,637188,831324,1080420,1398968,1805012,2320992,2974728,3800618

%N G.f.: Sum_{k>=1} x^(2*k)/(1-x^(2*k)) * Product_{k>=1} (1+x^k)/(1-x^k).

%C Convolution A066898 of and A000009.

%C Convolution A090867 of and A000041.

%H Vaclav Kotesovec, <a href="/A305104/b305104.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ (2*gamma + log(n/Pi^2)) * exp(Pi*sqrt(n)) / (16*Pi*sqrt(n)), where gamma is the Euler-Mascheroni constant A001620.

%t nmax = 50; CoefficientList[Series[Sum[x^(2*k)/(1-x^(2*k)), {k, 1, nmax}] * Product[(1+x^k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A015128, A066898, A090867, A305102, A305105.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, May 25 2018