A277468 E.g.f.: tanh(x)/(1+LambertW(-x)).

0, 1, 2, 10, 100, 1216, 17766, 309744, 6260360, 143641600, 3688352650, 104786813440, 3263080663404, 110514370068480, 4044232154193518, 159019302501971968, 6685886706336107536, 299315231931854749696, 14214873507079452102162, 713784039156929684963328

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, A277467.

Programs

Mathematica

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

PARI

x='x+O('x^50); concat([0], Vec(serlaplace(tanh(x)/(1 + lambertw(-x))))) \\ G. C. Greubel, Nov 05 2017

Formula

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