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%I #5 Jul 27 2019 03:58:57
%S 1,1,0,0,6,30,0,720,5760,0,362880,5417280,17107200,479001600,
%T 8885479680,32691859200,1307674368000,34151856076800,214585052774400,
%U 6402373705728000,192796754895360000,1542202547010048000,55105230485200896000,1944933030182596608000
%N E.g.f.: Product_{k>=1} (1 + x^(3*k-2) / (3*k-2)).
%H Vaclav Kotesovec, <a href="/A326858/b326858.txt">Table of n, a(n) for n = 0..440</a>
%F a(n) ~ n! / (3^(1/3) * Gamma(2/3) * exp(gamma/3) * 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-2)/(3*k-2)), {k, 1, Floor[nmax/3]+1}], {x, 0, nmax}], x] * Range[0, nmax]!
%Y Cf. A007838, A088994, A326756, A326857.
%K nonn
%O 0,5
%A _Vaclav Kotesovec_, Jul 27 2019