A013177 - OEIS

%I #10 Nov 29 2016 08:44:11

%S 2,16,560,42880,5692160,1158860800,335091660800,130514735104000,

%T 65860132462592000,41792278392537088000,32569972497977507840000,

%U 30580999289444580720640000,34048056335378925092864000000

%N tan(arctanh(x)+arctan(x))=2*x+16/3!*x^3+560/5!*x^5+42880/7!*x^7...

%F a(n) ~ (1-r^4) * (2*n+1)! / r^(2*n+2), where r = 0.734095513758912755828782788976924944882810535913453055562... is the root of the equation arctanh(r) + arctan(r) = Pi/2. Also root of equation Pi + log((1-r)/(1+r)) = arctan(2*r/(1-r^2)). - _Vaclav Kotesovec_, Feb 07 2015

%t nn = 20; Table[(CoefficientList[Series[Tan[ArcTan[x] + ArcTanh[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 07 2015 *)

%K nonn

%O 0,1

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