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%I #12 Nov 06 2017 02:42:11
%S 0,1,2,13,112,1321,19296,335637,6764864,154946449,3973820800,
%T 112789880413,3509627281920,118790978349369,4344883388878592,
%U 170767066282574821,7177162988688031744,321206181612447781921,15250250261039350358016,765586309042945067185581
%N E.g.f.: sinh(x)/(1+LambertW(-x)).
%H G. C. Greubel, <a href="/A277463/b277463.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) ~ sinh(exp(-1)) * n^n.
%t CoefficientList[Series[Sinh[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
%t Table[(1-(-1)^n + Sum[(1-(-1)^(n-k)) * Binomial[n,k] * k^k, {k, 1, n}])/2, {n, 0, 25}]
%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace(sinh(x)/(1 + lambertw(-x))))) \\ _G. C. Greubel_, Nov 05 2017
%Y Cf. A000312, A069856, A086331, A277461, A277464.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 16 2016
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