A285462 Expansion of Product_{k>=1} ((1 + x^(2*k)) / (1 - x^k))^k.

1, 1, 4, 7, 18, 32, 72, 127, 257, 454, 861, 1497, 2719, 4654, 8171, 13781, 23564, 39159, 65559, 107455, 176712, 286000, 463200, 740910, 1184123, 1873656, 2959376, 4636145, 7245680, 11246590, 17409731, 26792371, 41114202, 62769820, 95553779, 144803917

Offset: 0

Author

Vaclav Kotesovec, Apr 19 2017

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A156616, A285447, A285460, A285461.

Cf. A279328.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[((1+x^(2*k))/(1-x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(1/12 + 3 * (19*Zeta(3))^(1/3) * n^(2/3) / 4) * (19*Zeta(3))^(7/36) / (A * 2^(7/6) * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.