A277477 E.g.f.: -cos(x)*LambertW(-x).

0, 1, 2, 6, 52, 540, 6846, 104832, 1883848, 38889360, 907247770, 23608391840, 678039307452, 21305543325248, 727095737061526, 26781816978470400, 1059020025979194128, 44746083421419997440, 2011929587198990154162, 95918808101232854969856

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, A277462, A277473, A277475, A277478.

Programs

Mathematica

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

PARI

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

Formula

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