A012981 arctanh(arctan(x)+sin(x))=2*x+13/3!*x^3+553/5!*x^5+57839/7!*x^7...

2, 13, 553, 57839, 11359153, 3579398359, 1655031037177, 1054978773554159, 886822655405158113, 950463966040325692455, 1265021553451798971633001, 2047001827823001219625900543, 3957634961967849174268972586001

Offset

0,1

Links

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

Formula

a(n) ~ (2*n)! / r^(2*n+1), where r = 0.5343315247229429263511748056113294391694... is the root of the equation arctan(r)+sin(r) = 1. - Vaclav Kotesovec, Feb 05 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcTan[x] + Sin[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: A132570 A013048 A342958 * A154356 A013111 A179434

Adjacent sequences: A012978 A012979 A012980 * A012982 A012983 A012984

Keyword

nonn

Author

Patrick Demichel

Status

approved