A326857 E.g.f.: Product_{k>=1} (1 + x^(3*k-1) / (3*k-1)).
1, 0, 1, 0, 0, 24, 0, 504, 5040, 0, 226800, 3628800, 0, 438721920, 6227020800, 16345929600, 1127656857600, 20922789888000, 58203397324800, 6697914906009600, 121645100408832000, 655224745383936000, 51359276952023040000, 1124000727777607680000
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..440
- Vaclav Kotesovec, Graph - the asymptotic ratio (30000 terms)
Programs
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Mathematica
nmax = 30; CoefficientList[Series[Product[(1+x^(3*k-1)/(3*k-1)), {k, 1, Floor[nmax/3]+1}], {x, 0, nmax}], x] * Range[0, nmax]!
Formula
a(n) ~ 2 * Pi * n! / (exp(gamma/3) * 3^(5/6) * Gamma(1/3)^2 * n^(2/3)), where gamma is the Euler-Mascheroni constant A001620 and Gamma() is the Gamma function.