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%I #7 Jul 28 2019 12:45:47
%S 1,0,1,0,0,24,0,504,5040,0,226800,3628800,0,438721920,6227020800,
%T 16345929600,1127656857600,20922789888000,58203397324800,
%U 6697914906009600,121645100408832000,655224745383936000,51359276952023040000,1124000727777607680000
%N E.g.f.: Product_{k>=1} (1 + x^(3*k-1) / (3*k-1)).
%H Vaclav Kotesovec, <a href="/A326857/b326857.txt">Table of n, a(n) for n = 0..440</a>
%H Vaclav Kotesovec, <a href="/A326857/a326857.jpg">Graph - the asymptotic ratio (30000 terms)</a>
%F 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.
%t 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]!
%Y Cf. A007838, A088994, A326755, A326858.
%K nonn
%O 0,6
%A _Vaclav Kotesovec_, Jul 27 2019