A285460 Expansion of Product_{k>=1} ((1 + x^(4*k)) / (1 - x^k))^k.

1, 1, 3, 6, 14, 25, 51, 92, 175, 308, 554, 957, 1670, 2820, 4778, 7940, 13169, 21511, 35032, 56405, 90453, 143716, 227342, 356950, 557977, 866588, 1340109, 2060912, 3156274, 4810016, 7301490, 11034661, 16614681, 24916208, 37234864, 55440054, 82274277

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, A285462, A285447, A285461, A285472.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[((1+x^(4*k))/(1-x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(1/12 + 3 * 2^(-8/3) * (67*Zeta(3))^(1/3) * n^(2/3)) * (67*Zeta(3))^(7/36) / (A * 2^(14/9) * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.