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

0,6

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..440

Vaclav Kotesovec, Graph - the asymptotic ratio (30000 terms)

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.

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]!

Crossrefs

Cf. A007838, A088994, A326755, A326858.

Sequence in context: A364226 A128379 A111983 * A340135 A364203 A308304

Adjacent sequences: A326854 A326855 A326856 * A326858 A326859 A326860

Keyword

nonn

Author

Vaclav Kotesovec, Jul 27 2019

Status

approved