A009842 - OEIS

%I #13 Jun 22 2015 22:36:29

%S 0,1,0,-5,12,6,-120,442,-2352,13192,53280,-1665432,12223200,-6629648,

%T -706340544,9387463888,-95898673920,563447710848,8308014488064,

%U -283290718941056,3505513923832320,-9173243369732864,-499029405102412800

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

%F a(n) ~ n! * (2*cos(3*n*Pi/4)*(1 - exp(4) - 2*exp(2)*sin(2)) + 2*(1 - exp(4) + 2*exp(2)*sin(2))*sin(3*n*Pi/4)) / ((1 + exp(4) + 2*exp(2)*cos(2)) * 2^(1+n/2)). - _Vaclav Kotesovec_, Jan 24 2015

%t Tanh[ x ]/Cosh[ Log[ 1+x ] ]

%t CoefficientList[Series[(2*(1 + x)*Tanh[x])/(1 + (1 + x)^2), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 24 2015 *)

%K sign,easy

%O 0,4

%A _R. H. Hardin_

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