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%I #6 May 21 2019 02:47:48
%S 1,1,2,8,31,147,884,5567,39176,311400,2644490,24206327,239684768,
%T 2519262527,28077597357,331892965533,4130002336563,53944450834303,
%U 738940309779760,10577568411051305,157846971489443335,2452481386778640564,39589449956634478543
%N Expansion of e.g.f. exp(-1 + Product_{k>=1} (1 + x^k/k!)).
%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1)*A007837(k)*a(n-k).
%t nmax = 22; CoefficientList[Series[Exp[Product[(1 + x^k/k!), {k, 1, nmax}] - 1], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A007837, A143463, A182927, A308338.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, May 20 2019
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