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%I #6 Apr 23 2020 05:35:12
%S 1,0,-3,-8,45,576,385,-54144,-499527,4787200,160740261,558627840,
%T -45943496027,-854266871808,8403892043625,590895130771456,
%U 4982009666876145,-320936968832679936,-10133752613818727987,75595253378088960000,11587542472638176520861
%N E.g.f. A(x) satisfies: A(x) = x * exp(A(x)) * (1 - A(x)).
%C Exponential reversion of A000240 (rencontres numbers).
%H Vaclav Kotesovec, <a href="/A334316/b334316.txt">Table of n, a(n) for n = 1..400</a>
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = (n-1)! * Sum_{k=0..n-1} (-1)^k * binomial(n,k) * n^(n-k-1) / (n-k-1)!.
%t nmax = 21; CoefficientList[InverseSeries[Series[x Exp[-x]/(1 - x), {x, 0, nmax}], x], x] Range[0, nmax]! // Rest
%t Table[(n - 1)! Sum[(-1)^k Binomial[n, k] n^(n - k - 1)/(n - k - 1)!, {k, 0, n - 1}], {n, 1, 21}]
%t Table[HypergeometricU[1 - n, 2, n], {n, 1, 21}]
%Y Cf. A000240, A052885.
%K sign
%O 1,3
%A _Ilya Gutkovskiy_, Apr 22 2020
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