A012363 - OEIS

%I #9 Oct 24 2013 08:59:04

%S 0,1,2,7,36,285,2662,30147,395976,5968505,101054282,1901962687,

%T 39368308716,889051951125,21749632880302,573017429752827,

%U 16174993678778256,487024011982108145,15580632579831576722

%N arctanh(tan(x)*exp(x))=x+2/2!*x^2+7/3!*x^3+36/4!*x^4+285/5!*x^5...

%F a(n) ~ (n-1)!/(2*r^n), where r = 0.5313908566521572... is the root of the equation tan(r)*exp(r)=1. - _Vaclav Kotesovec_, Oct 24 2013

%t CoefficientList[Series[ArcTanh[Tan[x]*Exp[x]], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 24 2013 *)

%K nonn

%O 0,3

%A Patrick Demichel (patrick.demichel(AT)hp.com)

%E Prepended missing a(0)=0, _Vaclav Kotesovec_, Oct 24 2013