A292037 Expansion of Product_{k>=1} ((1 + x^(2*k-1)) / (1 - x^(2*k-1)))^k.

1, 2, 2, 6, 10, 16, 30, 46, 78, 124, 196, 306, 470, 724, 1086, 1644, 2438, 3608, 5304, 7734, 11232, 16196, 23270, 33206, 47250, 66846, 94232, 132280, 184966, 257720, 357768, 495090, 682702, 938760, 1286668, 1758708, 2397012, 3258340, 4417570, 5974204, 8059824

Offset: 0

Author

Vaclav Kotesovec, Sep 08 2017

Keywords

• nonn

Comments

Convolution of A263140 and A035528 (with a(0)=1).

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A035528, A080054, A263140, A292038.

Programs

Mathematica

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

Formula

a(n) ~ exp(-1/24 - Pi^4/(1344*Zeta(3)) + Pi^2 * n^(1/3) / (8*(7*Zeta(3))^(1/3)) + 3*(7*Zeta(3))^(1/3) * n^(2/3)/4) * A^(1/2) * (7*Zeta(3))^(11/72) / (2^(5/4) * sqrt(3*Pi) * n^(47/72)), where A is the Glaisher-Kinkelin constant A074962.