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%I #10 Jun 18 2018 19:19:04
%S 1,1,2,8,30,156,900,6192,47904,422928,4138848,44864640,531227520,
%T 6836927040,94891046400,1413494219520,22481104677120,380261238681600,
%U 6814832064422400,128991143627965440,2571187988206540800,53834676521793638400,1181214133296983654400
%N Expansion of Product_{k>=1} (1 + k!*x^k).
%H Vaclav Kotesovec, <a href="/A265950/b265950.txt">Table of n, a(n) for n = 0..440</a>
%F a(n) ~ n! * (1 + 1/n + 2/n^2 + 10/n^3 + 56/n^4 + 394/n^5 + 3332/n^6 + 32782/n^7 + 368072/n^8 + 4651666/n^9 + 65440748/n^10 + ...), for coefficients see A265954.
%F G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^(k+1)*(j!)^k*x^(j*k)/k). - _Ilya Gutkovskiy_, Jun 18 2018
%t nmax=30; CoefficientList[Series[Product[(1+k!*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A077365, A265954.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Dec 19 2015
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