A013177 tan(arctanh(x)+arctan(x))=2*x+16/3!*x^3+560/5!*x^5+42880/7!*x^7...

2, 16, 560, 42880, 5692160, 1158860800, 335091660800, 130514735104000, 65860132462592000, 41792278392537088000, 32569972497977507840000, 30580999289444580720640000, 34048056335378925092864000000

Offset

0,1

Links

Table of n, a(n) for n=0..12.

Formula

a(n) ~ (1-r^4) * (2*n+1)! / r^(2*n+2), where r = 0.734095513758912755828782788976924944882810535913453055562... is the root of the equation arctanh(r) + arctan(r) = Pi/2. Also root of equation Pi + log((1-r)/(1+r)) = arctan(2*r/(1-r^2)). - Vaclav Kotesovec, Feb 07 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[ArcTan[x] + ArcTanh[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 07 2015 *)

Crossrefs

Sequence in context: A013004 A012679 A012726 * A060279 A369674 A012757

Adjacent sequences: A013174 A013175 A013176 * A013178 A013179 A013180

Keyword

nonn

Author

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

Status

approved