A012849 arctanh(sec(x)*arctanh(x))=x+7/3!*x^3+193/5!*x^5+13319/7!*x^7...

1, 7, 193, 13319, 1721281, 357281351, 108706678273, 45591739883975, 25211971076762753, 17775279702237604231, 15562493015528998511681, 16565188691481564795512967, 21067308092979783990029042241

Offset

0,2

Links

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

Formula

a(n) ~ (2*n)! / r^(2*n+1), where r = 0.6588155299144662008044917663989656738607... is the root of the equation sec(r)*arctanh(r) = 1. - Vaclav Kotesovec, Feb 05 2015

Mathematica

With[{nn=30}, Take[CoefficientList[Series[ArcTanh[Sec[x]ArcTanh[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Jan 03 2014 *)

Crossrefs

Sequence in context: A024096 A030257 A159826 * A308610 A277420 A220754

Adjacent sequences: A012846 A012847 A012848 * A012850 A012851 A012852

Keyword

nonn

Author

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

Extensions

Definition clarified by Harvey P. Dale, Jan 03 2014

Status

approved