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%I #10 Nov 08 2017 02:31:57
%S 0,1,2,11,104,1249,18264,318163,6425152,147344769,3781848480,
%T 107408279483,3343875651456,113227469886881,4142804357946240,
%U 162871544915116035,6847004160475236352,306495323034774157569,14554502490109085839872,730777840212988501198059
%N E.g.f.: arcsinh(x)/(1+LambertW(-x)).
%H G. C. Greubel, <a href="/A277470/b277470.txt">Table of n, a(n) for n = 0..385</a>
%F a(n) ~ arcsinh(exp(-1)) * n^n.
%F a(n) ~ (-1 + log(1 + sqrt(1+exp(2)))) * n^n.
%t CoefficientList[Series[ArcSinh[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
%t Flatten[{0, Table[Sin[Pi*n/2] * (n-2)!!^2 + Sum[Sin[Pi*k/2] * Binomial[n, k] * (k-2)!!^2 * (n-k)^(n-k), {k, 1, n-1}], {n, 1, 25}]}] (* _Vaclav Kotesovec_, Oct 28 2016 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace(asinh(x)/(1 + lambertw(-x)) ))) \\ _G. C. Greubel_, Nov 07 2017
%Y Cf. A000312, A086331, A277469.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 16 2016
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