%I #9 Jul 14 2024 13:51:21
%S 2,19,1025,138129,34734545,14037224089,8320152726665,6799527662204049,
%T 7327672308214372385,10068470883926665540009,
%U 17180000319605942481431705,35640287243130630709541583969
%N arctanh(sinh(x)+tan(x))=2*x+19/3!*x^3+1025/5!*x^5+138129/7!*x^7...
%F a(n) ~ (2*n)! / r^(2*n+1), where r = 0.47191303538345047716706116017105574144998... is the root of the equation sinh(r)+tan(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015
%t nn = 20; Table[(CoefficientList[Series[ArcTanh[Sinh[x] + Tan[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 05 2015 *)
%t With[{nn=30},Take[CoefficientList[Series[ArcTanh[Sinh[x]+Tan[x]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Jul 14 2024 *)
%K nonn
%O 0,1
%A Patrick Demichel (patrick.demichel(AT)hp.com)