A277469 E.g.f.: arcsin(x)/(1 + LambertW(-x)).

0, 1, 2, 13, 112, 1329, 19344, 336533, 6778752, 155247777, 3980956800, 112984562813, 3515475849216, 118984054897681, 4351800687259648, 171034439586509445, 7188243684485414912, 321696219477456836929, 15273278824827215388672, 766732102664665113137517

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, A277470.

Programs

Mathematica

CoefficientList[Series[ArcSin[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
Flatten[{0, Table[(1-(-1)^n)/2 * (n-2)!!^2 + Sum[Binomial[n, k] * (1-(-1)^k)/2 * (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(asin(x)/(1 + lambertw(-x))))) \\ G. C. Greubel, Nov 07 2017

Formula

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