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%I #10 Nov 13 2017 02:46:34
%S 0,1,4,21,148,1365,15966,229411,3932440,78438681,1784386810,
%T 45565679511,1289796524820,40065439945141,1354630932486118,
%U 49512390012682395,1945119744809765296,81728227537432878513,3657019655412488345202,173610723750748520091679
%N E.g.f.: -LambertW(-x)/(1-x).
%H G. C. Greubel, <a href="/A277505/b277505.txt">Table of n, a(n) for n = 0..385</a>
%F For n > 0, a(n) = Sum_{k=1..n} binomial(n,k) * k^(k-1) * (n-k)!.
%F a(n) ~ n^(n-1) / (1-exp(-1)).
%t CoefficientList[Series[-LambertW[-x]/(1-x), {x, 0, 20}], x] * Range[0, 20]!
%t Flatten[{0, Table[Sum[Binomial[n, k]*k^(k-1)*(n-k)!, {k, 1, n}], {n, 1, 20}]}]
%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace(-lambertw(-x)/(1-x)))) \\ _G. C. Greubel_, Nov 12 2017
%Y Cf. A000169, A277511.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 18 2016
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