A013111 arctanh(arcsinh(x)+arctan(x))=2*x+13/3!*x^3+561/5!*x^5+58959/7!*x^7...

2, 13, 561, 58959, 11644353, 3689490231, 1715357184849, 1099472915829519, 929329108531548417, 1001522171480774224743, 1340339793936610136490513, 2180857643900986608848041983, 4239717441519601414508854360257

Offset

0,1

Links

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

Formula

a(n) ~ (2*n)! / r^(2*n+1), where r = 0.53286199991370386509144685314983925384646... is the root of the equation arcsinh(r)+arctan(r) = 1. - Vaclav Kotesovec, Feb 05 2015

Mathematica

With[{nn=30}, Take[CoefficientList[Series[ArcTanh[ArcSinh[x]+ArcTan[x]], {x, 0, nn}], x]Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Nov 02 2011 *)

Crossrefs

Sequence in context: A342958 A012981 A154356 * A179434 A101342 A119122

Adjacent sequences: A013108 A013109 A013110 * A013112 A013113 A013114

Keyword

nonn

Author

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

Status

approved