A013087 - OEIS

%I #7 Feb 07 2015 06:13:16

%S 2,16,530,37840,4665890,880829200,236051798450,85184059714000,

%T 39823482623005250,23410203659063338000,16900988192636551591250,

%U 14700311020824054699970000,15161633552176216519055281250

%N tan(arcsinh(x)+arcsin(x))=2*x+16/3!*x^3+530/5!*x^5+37840/7!*x^7...

%F a(n) ~ 2 * sqrt(1-r^4) * (2*n+1)! / ((sqrt(1-r^2) + sqrt(1+r^2)) * r^(2*n+2)), where r = 0.762718149449013683089118440018621705719487630300437769993... is the root of the equation arcsinh(r) + arcsin(r) = Pi/2. - _Vaclav Kotesovec_, Feb 07 2015

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