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%I #13 Dec 24 2015 07:50:26
%S 1,1,6,39,328,3305,39396,536053,8210784,139670721,2612934820,
%T 53260680341,1175587507392,27929705129521,710678763809028,
%U 19284199100275845,555961318128936256,16972543570002866945,547046699544108738756,18566047855851466092949
%N E.g.f.: Product_{k>=1} 1/(1 - exp(x)*x^k).
%H Vaclav Kotesovec, <a href="/A265953/b265953.txt">Table of n, a(n) for n = 0..408</a>
%F a(n) ~ c * n! / LambertW(1)^n, where c = 1/(1 + LambertW(1)) * Product_{j>=1} 1/(1 - LambertW(1)^j) = 3.40413121452412914124892504613759007312040569..., LambertW(1) = A030178.
%t nmax=20; CoefficientList[Series[Product[1/(1-E^x*x^k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
%Y Cf. A030178, A030797, A265952.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Dec 19 2015
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