A285458 Expansion of Product_{k>=1} ((1 + x^k) / (1 - x^(4*k)))^k.
1, 1, 2, 5, 9, 17, 30, 54, 94, 161, 269, 449, 740, 1200, 1930, 3083, 4877, 7650, 11919, 18444, 28363, 43341, 65848, 99523, 149654, 223901, 333448, 494427, 729996, 1073408, 1572264, 2294389, 3336191, 4834261, 6981727, 10050944, 14424665, 20639641, 29447118
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^(4*k)))^k, {k, 1, nmax}], {x, 0, nmax}], x]
Formula
a(n) ~ exp(1/12 + 3 * (13*Zeta(3))^(1/3) * n^(2/3) / 4) * (13*Zeta(3))^(7/36) / (2 * A * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.