A013106 - OEIS

%I #7 Feb 07 2015 06:19:45

%S 2,13,305,15055,1273025,164517175,30146073425,7436961751375,

%T 2376178127194625,954639310366870375,470988100516584340625,

%U 279956419390270100749375,197317558974617657009890625

%N tan(arcsinh(x)+arctan(x))=2*x+13/3!*x^3+305/5!*x^5+15055/7!*x^7...

%F a(n) ~ 2 * (1+r^2) * (2*n+1)! / ((1 + sqrt(1+r^2)) * r^(2*n+2)), where r = 0.92264952178798498452267332008203354064529018007517530562577... is the root of the equation arcsinh(r) + arctan(r) = Pi/2. - _Vaclav Kotesovec_, Feb 07 2015

%t nn = 20; Table[(CoefficientList[Series[Tan[ArcSinh[x] + ArcTan[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)