A277501 E.g.f.: -LambertW(-tanh(x)).

0, 1, 2, 7, 48, 461, 5488, 79171, 1347328, 26396185, 585025024, 14473813311, 395433660416, 11824374817893, 384118189803520, 13470784014801787, 507233444671848448, 20411081546839908401, 874130806090067607552, 39696948293418345150327

Offset: 0

Author

Vaclav Kotesovec, Oct 18 2016

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..389

Crossrefs

Cf. A238085, A277468, A277480, A277500.

Programs

Mathematica

CoefficientList[Series[-LambertW[-Tanh[x]], {x, 0, 20}], x] * Range[0, 20]!

PARI

x='x+O('x^10); concat([0], Vec(serlaplace(-lambertw(-tanh(x))))) \\ G. C. Greubel, Nov 09 2017

Formula

a(n) ~ sqrt(1-exp(-2)) * 2^(n-1/2) * (log((exp(1)+1)/(exp(1)-1)))^(1/2-n) * exp(1/2-n) * n^(n-1).