A013040 - OEIS

%I #7 Feb 05 2015 16:05:09

%S 2,18,938,122066,29635154,11561687346,6615385296570,5218960553242866,

%T 5429404407724397474,7201623832416658882514,

%U 11862352305394237757311946,23755795427038939521773734290

%N arctanh(sinh(x)+arcsin(x))=2*x+18/3!*x^3+938/5!*x^5+122066/7!*x^7...

%F a(n) ~ (2*n)! / r^(2*n+1), where r = 0.4803099786153606144946517326733725892405... is the root of the equation sinh(r)+arcsin(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015

%t nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSin[x] + Sinh[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 05 2015 *)

%K nonn

%O 0,1

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