A012618 - OEIS

%I #9 Oct 31 2013 12:07:37

%S 0,2,4,350,7208,1520218,106485740,38051376246,6123846322896,

%T 3217389043510578,964215477538459732,692917532440212444686,

%U 338776184246581290006520,318786053587029917056642186

%N arctanh(arcsinh(x)*tan(x))=2/2!*x^2+4/4!*x^4+350/6!*x^6+7208/8!*x^8...

%F a(n) ~ (2*n-1)! / r^(2*n), where r = 0.89357177742189289... is the root of the equation r+sqrt(r^2+1) = exp(1/tan(r)). - _Vaclav Kotesovec_, Oct 31 2013

%t Table[n!*SeriesCoefficient[ArcTanh[ArcSinh[x]*Tan[x]],{x,0,n}],{n,0,40,2}] (* _Vaclav Kotesovec_, Oct 31 2013 *)

%K nonn

%O 0,2

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

%E Prepended missing a(0)=0 from _Vaclav Kotesovec_, Oct 31 2013