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%I #10 Nov 08 2017 02:29:33
%S 0,1,0,6,36,380,4830,74382,1342712,27825912,651274650,16994464850,
%T 489240628932,15404364096420,526634857318934,19428038813967630,
%U 769280055136105200,32543192449030871792,1464827827285673677746,69903432558329996409642,3525344776953738276010940
%N E.g.f.: -exp(-x)*LambertW(-x).
%H G. C. Greubel, <a href="/A277474/b277474.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) = Sum_{k=1..n} (-1)^(n-k) * binomial(n,k) * k^(k-1).
%F a(n) ~ exp(-exp(-1)) * n^(n-1).
%t CoefficientList[Series[-Exp[-x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
%t Table[Sum[(-1)^(n-k)*Binomial[n, k]*k^(k-1), {k, 1, n}], {n, 0, 20}]
%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace(-exp(-x)*lambertw(-x)))) \\ _G. C. Greubel_, Nov 07 2017
%Y Cf. A000169, A069856, A086331, A277473.
%K nonn
%O 0,4
%A _Vaclav Kotesovec_, Oct 17 2016
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