A012791 arctanh(sec(x)*arcsin(x))=x+6/3!*x^3+148/5!*x^5+9184/7!*x^7...

1, 6, 148, 9184, 1066640, 199000736, 54431471040, 20523724218880, 10203766053312768, 6467780044492713472, 5090997086675585360896, 4871968356294907783585792, 5570589015199967686042095616

Offset

0,2

Links

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

Formula

a(n) ~ (2*n)! / r^(2*n+1), where r = 0.6948196907307875655784200727751937626855... is the root of the equation sec(r)*arcsin(r) = 1. - Vaclav Kotesovec, Feb 05 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[ArcTanh[ArcSin[x]*Sec[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: A065986 A375780 A199226 * A347842 A264645 A089480

Adjacent sequences: A012788 A012789 A012790 * A012792 A012793 A012794

Keyword

nonn

Author

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

Status

approved