A326756 E.g.f.: Product_{k>=1} 1/(1 - x^(3*k-2)/(3*k-2)).

1, 1, 2, 6, 30, 150, 900, 7020, 58680, 528120, 5644080, 63510480, 769610160, 10483933680, 150733677600, 2272680828000, 37752297264000, 653710445308800, 11839468023187200, 231623795388268800, 4723930089495302400, 99779582243860358400, 2249431677071465356800

Offset: 0

Author

Vaclav Kotesovec, Jul 23 2019

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..447
• D. H. Lehmer, On reciprocally weighted partitions, Acta Arithmetica XXI (1972), 379-388 (Theorem 7).

Crossrefs

Cf. A007841, A294506, A309319, A326755.

Programs

Mathematica

nmax = 25; CoefficientList[Series[1/Product[(1-x^(3*k-2)/(3*k-2)), {k, 1, Floor[nmax/3] + 1}], {x, 0, nmax}], x] * Range[0, nmax]!

Formula

a(n) ~ 3^(5/3) * exp(-gamma/3) * n^(1/3) * n! / Gamma(1/3)^2, where gamma is the Euler-Mascheroni constant A001620 and Gamma() is the Gamma function [Lehmer, 1972]. - Vaclav Kotesovec, Jul 23 2019