A277462 E.g.f.: cos(x)/(1 + LambertW(-x)).

1, 1, 3, 24, 233, 2860, 42875, 758856, 15488657, 358164432, 9254769459, 264273873600, 8264362186489, 280896392748608, 10310601442639147, 406479520869636480, 17129450693008029729, 768404013933189112064, 36557893891263190204259, 1838650651518153170939904

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, A277461, A277464.

Programs

Mathematica

CoefficientList[Series[Cos[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
Table[Cos[Pi*n/2] + Sum[Binomial[n, k] * Cos[Pi*(n-k)/2] * k^k, {k, 1, n}], {n, 0, 25}] (* Vaclav Kotesovec, Oct 28 2016 *)

PARI

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

Formula

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