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%I #7 Nov 08 2017 02:32:12
%S 0,0,2,6,40,340,3936,56714,976704,19535688,444743680,11349643822,
%T 320813048832,9947821243100,335700998830848,12246806941654770,
%U 480247532548624384,20144008859005187344,899923326921333301248,42658767419625168409814,2138475182252830504796160
%N E.g.f.: -sinh(x)*LambertW(-x).
%H G. C. Greubel, <a href="/A277476/b277476.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) = Sum_{k=1..n} (1 - (-1)^(n-k)) * binomial(n,k) * k^(k-1)/2.
%F a(n) ~ sinh(exp(-1)) * n^(n-1).
%t CoefficientList[Series[-Sinh[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
%t Table[Sum[(1 - (-1)^(n-k)) * Binomial[n, k] * k^(k-1)/2, {k, 1, n}], {n, 0, 20}]
%o (PARI) x='x+O('x^50); concat([0,0], Vec(serlaplace(-sinh(x)*lambertw(-x) ))) \\ _G. C. Greubel_, Nov 07 2017
%Y Cf. A000169, A277463, A277473, A277475, A277478.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 17 2016
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