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%I #8 Jul 31 2019 12:37:21
%S 1,2,8,48,364,3320,35464,433692,5962548,90931152,1522657264,
%T 27765229844,547487475484,11604952395816,263091290017560,
%U 6351255101776812,162643987129698628,4403250400372110656,125649232950852714496,3769013390615951560068,118555772298034094231724
%N E.g.f.: Product_{k>=1} (1 + (exp(x)-1)^k/k) / (1 - (exp(x)-1)^k/k).
%H Vaclav Kotesovec, <a href="/A326887/b326887.txt">Table of n, a(n) for n = 0..420</a>
%F a(n) = Sum_{k=0..n} A305199(k)*Stirling2(n,k).
%F a(n) ~ n * (n+1)! / (16 * exp(2*gamma) * log(2)^(n+3)), where gamma is the Euler-Mascheroni constant A001620.
%t nmax = 20; CoefficientList[Series[Product[(1+(Exp[x]-1)^k/k)/(1-(Exp[x]-1)^k/k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
%Y Cf. A305199, A305986, A305987.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jul 31 2019
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