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%I #10 Nov 13 2017 02:48:43
%S 0,1,0,9,28,485,4866,83587,1428456,30190617,698093830,18258392471,
%T 523907661036,16487285529013,562892775847962,20749534387671195,
%U 820928954404107856,34705399650797034929,1561214366024349903246,74464277343448593371167,3753594453131028132576660
%N E.g.f.: -LambertW(-x)/(1+x).
%H G. C. Greubel, <a href="/A277511/b277511.txt">Table of n, a(n) for n = 0..385</a>
%F For n > 0, a(n) = Sum_{k=1..n} (-1)^(n-k) * 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[(-1)^(n-k) * 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, A277505.
%K nonn
%O 0,4
%A _Vaclav Kotesovec_, Oct 18 2016
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