A285289 Expansion of Product_{k>=1} ((1 + x^k) / (1 + x^(2*k)))^k.
1, 1, 1, 4, 5, 10, 16, 26, 44, 68, 110, 167, 265, 399, 609, 919, 1371, 2040, 3005, 4420, 6436, 9364, 13501, 19433, 27806, 39639, 56265, 79572, 112126, 157390, 220283, 307163, 427145, 592029, 818359, 1127878, 1550483, 2125656, 2907013, 3965853, 5397497
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
nmax = 50; CoefficientList[Series[Product[((1+x^k)/(1+x^(2*k)))^k, {k, 1, nmax}], {x, 0, nmax}], x]
Formula
a(n) ~ exp(3^(5/3) * Zeta(3)^(1/3) * n^(2/3) / 4) * Zeta(3)^(1/6) / (2 * 3^(1/6) * sqrt(Pi) * n^(2/3)).