A277483 E.g.f.: -arcsin(x)*LambertW(-x).

0, 0, 2, 6, 40, 340, 3984, 57050, 982528, 19616328, 446355840, 11384327438, 321701896704, 9973046260060, 336499112011776, 12274383608508450, 481282311712489472, 20185816487436968208, 901732370496365076480, 42742176871086712813974, 2142556308913381810012160

Offset: 0

Author

Vaclav Kotesovec, Oct 17 2016

Keywords

• nonn

Links

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

Crossrefs

Cf. A000169, A277469, A277473, A277484.

Programs

Mathematica

CoefficientList[Series[-ArcSin[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Flatten[{0, Table[Sum[Binomial[n, k] * (1-(-1)^k)/2 * (k-2)!!^2 * (n-k)^(n-k-1), {k, 1, n-1}], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 28 2016 *)

PARI

x='x+O('x^50); concat([0,0], Vec(serlaplace(- asin(x)*lambertw(-x) ))) \\ G. C. Greubel, Nov 08 2017

Formula

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