%I #13 Nov 03 2013 10:50:39
%S 2,-8,82592,-608724608,22327881339392,-1873956615576209408,
%T 347762137588896627924992,-121417393113776577986657681408,
%U 73797732351936752045312739712827392,-72816242431281104821128628533638537412608,110758942324721681029366683611691936115004014592
%N arcsinh(tanh(x)*tan(x)) = 2/2!*x^2-8/6!*x^6+82592/10!*x^10...
%F Lim sup n->infinity (|a(n)|/(4*n)!)^(1/(4*n)) = 0.9003163161571... = abs(1/r), where r is the complex root of the equation sin(r)*(exp(2*r)-1) = I*cos(r)*(exp(2*r)+1). - _Vaclav Kotesovec_, Nov 02 2013
%t With[{nn=30},Take[CoefficientList[Series[ArcSinh[Tanh[x]Tan[x]],{x,0,nn}],x] Range[0,nn]!,{3,-1,4}]] (* _Harvey P. Dale_, Aug 08 2013 *)
%K sign
%O 0,1
%A Patrick Demichel (patrick.demichel(AT)hp.com)