A012849 - OEIS

%I #8 Feb 05 2015 15:41:12

%S 1,7,193,13319,1721281,357281351,108706678273,45591739883975,

%T 25211971076762753,17775279702237604231,15562493015528998511681,

%U 16565188691481564795512967,21067308092979783990029042241

%N arctanh(sec(x)*arctanh(x))=x+7/3!*x^3+193/5!*x^5+13319/7!*x^7...

%F a(n) ~ (2*n)! / r^(2*n+1), where r = 0.6588155299144662008044917663989656738607... is the root of the equation sec(r)*arctanh(r) = 1. - _Vaclav Kotesovec_, Feb 05 2015

%t With[{nn=30},Take[CoefficientList[Series[ArcTanh[Sec[x]ArcTanh[x]],{x,0,nn}],x] Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Jan 03 2014 *)

%K nonn

%O 0,2

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

%E Definition clarified by _Harvey P. Dale_, Jan 03 2014