A305121 G.f.: Sum_{k>=1} x^(2*k)/(1+x^(2*k)) * Product_{k>=1} 1/(1-x^k).

0, 0, 1, 1, 2, 3, 7, 9, 14, 20, 32, 43, 63, 85, 122, 162, 221, 292, 396, 514, 680, 878, 1147, 1465, 1886, 2391, 3050, 3836, 4841, 6048, 7579, 9403, 11685, 14419, 17806, 21845, 26810, 32725, 39947, 48528, 58926, 71267, 86151, 103750, 124860, 149791, 179551

Offset: 0

Author

Vaclav Kotesovec, May 26 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A006128, A209423, A066898, A066897, A305123.

Cf. A116680, A305122.

Programs

Mathematica

nmax = 60; CoefficientList[Series[Sum[x^(2*k)/(1+x^(2*k)), {k, 1, nmax}] * Product[1/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

For n > 0, a(n) = A209423(n) - A305123(n).

a(n) ~ log(2) * exp(Pi*sqrt(2*n/3)) / (2^(5/2)*Pi*sqrt(n)).