A013005 arctanh(arctan(x)+tan(x))=2*x+16/3!*x^3+808/5!*x^5+98432/7!*x^7...

2, 16, 808, 98432, 22498432, 8253398272, 4441967893504, 3295980115392512, 3225082749950656512, 4023514822062532460544, 6233513843421340514123776, 11741363464465799639674126336

Offset

0,1

Links

Table of n, a(n) for n=0..11.

Formula

a(n) ~ (2*n)! / r^(2*n+1), where r = 0.4952542103931914966377065988697787139312... is the root of the equation arctan(r)+tan(r) = 1. - Vaclav Kotesovec, Feb 05 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcTan[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 *)

Crossrefs

Sequence in context: A013088 A013137 A013990 * A013000 A013178 A306000

Adjacent sequences: A013002 A013003 A013004 * A013006 A013007 A013008

Keyword

nonn

Author

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

Status

approved