A012388 - OEIS

%I #7 Feb 08 2015 05:53:12

%S 0,2,16,392,21376,2117792,333550336,76433892992,23981418704896,

%T 9862199971860992,5144452992189485056,3317894031273853601792,

%U 2591931617534673513250816,2411532576645611695219515392

%N arcsin(tan(x)*tan(x))=2/2!*x^2+16/4!*x^4+392/6!*x^6+21376/8!*x^8...

%F a(n) ~ 2^(4*n-1) * (2*n)! / (n^(3/2) * Pi^(2*n)). - _Vaclav Kotesovec_, Feb 08 2015

%t nn = 20; Table[(CoefficientList[Series[ArcSin[Tan[x]^2], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* _Vaclav Kotesovec_, Feb 08 2015 *)

%K nonn

%O 0,2

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

%E a(0)=0 prepended by _Vaclav Kotesovec_, Feb 08 2015