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%I #13 Jul 17 2022 23:30:56
%S 0,1,4,18,116,1060,12702,187810,3296120,66897288,1540762010,
%T 39693752494,1130866726596,35300006582620,1198036854980630,
%U 43921652697277170,1729775120233353968,72831210167041246480,3264674481128340280242,155220967397580333229270
%N E.g.f.: -exp(x)*LambertW(-x).
%H G. C. Greubel, <a href="/A277473/b277473.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) = Sum_{k=1..n} 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[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_, Jun 11 2017
%Y Cf. A000169, A069856, A086331, A277474.
%Y Partial sums of A038051.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 17 2016
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