A009399 - OEIS

%I #17 Dec 21 2017 17:29:12

%S 0,2,-20,576,-33312,3258880,-485139456,102300807168,-29028932390912,

%T 10668077137133568,-4929291212351078400,2797060130323340197888,

%U -1912137417504544127975424,1550018044651811766917922816

%N Expansion of log(1+tanh(x)*x).

%F 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

%t 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 *)

%Y Cf. A009379, A069855, A085984.

%K sign

%O 0,2

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997

%E Prior Mathematica program replaced by _Harvey P. Dale_, Jun 13 2016