A277467 E.g.f.: tan(x)/(1+LambertW(-x)).

0, 1, 2, 14, 116, 1376, 19926, 346128, 6964712, 159396352, 4085415850, 115906440704, 3605365584732, 121998144397312, 4461190462108030, 175305587376883712, 7366747721719011280, 329646098258032459776, 15649117182518598570834, 785528920149992297070592

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, A277468.

Programs

Mathematica

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

PARI

x='x+O('x^30); concat([0], Vec(serlaplace(tan(x)/(1 + lambertw(-x))))) \\ G. C. Greubel, May 29 2018

Formula

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