A305104 G.f.: Sum_{k>=1} x^(2*k)/(1-x^(2*k)) * Product_{k>=1} (1+x^k)/(1-x^k).

0, 0, 1, 2, 6, 12, 24, 44, 79, 134, 222, 358, 566, 876, 1334, 2000, 2960, 4326, 6253, 8946, 12680, 17816, 24832, 34352, 47192, 64404, 87354, 117796, 157976, 210764, 279812, 369744, 486413, 637188, 831324, 1080420, 1398968, 1805012, 2320992, 2974728, 3800618

Offset: 0

Author

Vaclav Kotesovec, May 25 2018

Keywords

• nonn

Comments

Convolution A066898 of and A000009.

Convolution A090867 of and A000041.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

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

Programs

Mathematica

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]

Formula

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