A009399 Expansion of log(1+tanh(x)*x).

0, 2, -20, 576, -33312, 3258880, -485139456, 102300807168, -29028932390912, 10668077137133568, -4929291212351078400, 2797060130323340197888, -1912137417504544127975424, 1550018044651811766917922816

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Crossrefs

Cf. A009379, A069855, A085984.

Programs

Mathematica

With[{nn=30},Take[CoefficientList[Series[Log[1+Tanh[x]*x],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Jun 13 2016 *)

Formula

a(n) ~ -(-1)^n * sqrt(Pi) * 2^(2*n + 1) * n^(2*n - 1/2) / (r^(2*n) * exp(2*n)), where r = A069855 = 0.8603335890193797624838934241376623334118843632... is the root of the equation r * tan(r) = 1. - Vaclav Kotesovec, Dec 21 2017

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Prior Mathematica program replaced by Harvey P. Dale, Jun 13 2016