A277479 E.g.f.: -tan(x)*LambertW(-x).

0, 0, 2, 6, 44, 360, 4206, 59584, 1021432, 20329344, 461596090, 11756157952, 331835099364, 10278341179392, 346555737301606, 12633922368061440, 495139124241620080, 20758413862397509632, 926980786260912379122, 43925328338613823078400, 2201264843743619567644700

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, A277467, A277473, A277480.

Programs

Mathematica

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

PARI

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

Formula

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