A012798 - OEIS

%I #7 Feb 05 2015 15:29:34

%S 1,7,185,12367,1558865,316097527,94003171145,38543705698687,

%T 20840298552277025,14366953364916735847,12299504390976449116505,

%U 12801737583190675819689007,15920156445351352463114729585

%N arctanh(sec(x)*tan(x))=x+7/3!*x^3+185/5!*x^5+12367/7!*x^7...

%F a(n) ~ (2*n)! / (arctan(sqrt((sqrt(5)-1)/2)))^(2*n+1). - _Vaclav Kotesovec_, Feb 05 2015

%t nn = 20; Table[(CoefficientList[Series[ArcTanh[Sec[x]*Tan[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* _Vaclav Kotesovec_, Feb 05 2015 *)

%K nonn

%O 0,2

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