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%I #18 Sep 13 2018 03:04:26
%S 1,1,4,15,82,475,3456,26719,239996,2313609,24846640,285861301,
%T 3586817928,47988744115,690525294018,10547453864445,171595180564816,
%U 2949836193259105,53630566660122696,1025856767305899229,20638503314068334480
%N E.g.f.: Product_{n>=1} 1/(1 - x^n/n!)^n.
%C Compare to the e.g.f. of A032315: Product_{n>=1} (1 + x^n/n!)^n.
%H Vaclav Kotesovec, <a href="/A174661/b174661.txt">Table of n, a(n) for n = 0..380</a>
%F a(n) ~ c * n!, where c = product_{k>=2} 1/(1-1/k!)^k = 8.6304199482678945455168174204973507297310235756... . - _Vaclav Kotesovec_, Nov 03 2014
%F E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} j*x^(j*k)/(k*(j!)^k)). - _Ilya Gutkovskiy_, Sep 12 2018
%e E.g.f.: A(x) = 1 + x + 4*x^2/2! + 15*x^3/3! + 82*x^4/4! + ...;
%e A(x) = 1/((1-x)*(1-x^2/2!)^2*(1-x^3/3!)^3*(1-x^4/4!)^4*(1-x^5/5!)^5* ...).
%o (PARI) {a(n)=n!*polcoeff(prod(k=1,n,1/(1-x^k/k!+x*O(x^n))^k),n)}
%Y Cf. variant: A032315.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 30 2010
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