A277461 E.g.f.: sin(x)/(1+LambertW(-x)).

0, 1, 2, 11, 104, 1241, 18216, 317715, 6414848, 147107953, 3776164000, 107253230171, 3339157316736, 113070818225353, 4137170839854976, 162653198951193059, 6837934005096620032, 306093463368534049761, 14535589272368159900160, 729835620496621069643179

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, A277462, A277463.

Programs

Mathematica

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

PARI

x = 'x + O('x^30); concat(0, Vec(serlaplace(sin(x)/(1+lambertw(-x))))) \\ Michel Marcus, Jun 12 2017

Formula

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