A277470 E.g.f.: arcsinh(x)/(1+LambertW(-x)).

0, 1, 2, 11, 104, 1249, 18264, 318163, 6425152, 147344769, 3781848480, 107408279483, 3343875651456, 113227469886881, 4142804357946240, 162871544915116035, 6847004160475236352, 306495323034774157569, 14554502490109085839872, 730777840212988501198059

Offset: 0

Author

Vaclav Kotesovec, Oct 16 2016

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..385

Crossrefs

Cf. A000312, A086331, A277469.

Programs

Mathematica

CoefficientList[Series[ArcSinh[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
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 *)

PARI

x='x+O('x^50); concat([0], Vec(serlaplace(asinh(x)/(1 + lambertw(-x)) ))) \\ G. C. Greubel, Nov 07 2017

Formula

a(n) ~ arcsinh(exp(-1)) * n^n.

a(n) ~ (-1 + log(1 + sqrt(1+exp(2)))) * n^n.