A012746 arctanh(arctanh(x)*cos(x)) = x+1/3!*x^3+13/5!*x^5+677/7!*x^7+54937/9!*x^9...

1, 1, 13, 677, 54937, 6248713, 988579109, 212756765101, 60179200959793, 21632158018229009, 9619077100099258429, 5182270736688171740085, 3326876613520624630798281, 2509818428217896837411045913, 2198676694008933148388904662357, 2213672191262297018716557756353725

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

a(n) ~ (2*n)! / r^(2*n+1), where r = 0.932706009172514... is the root of the equation cos(r)*log((1-r)/(1+r)) = -2. - Vaclav Kotesovec, Nov 02 2013

Mathematica

Table[n!*SeriesCoefficient[ArcTanh[ArcTanh[x]*Cos[x]], {x, 0, n}], {n, 1, 41, 2}] (* Vaclav Kotesovec, Nov 02 2013 *)
With[{nn=40}, Take[CoefficientList[Series[ArcTanh[ArcTanh[x]Cos[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, May 20 2016 *)

Crossrefs

Sequence in context: A298951 A157027 A042307 * A211094 A290166 A113093

Adjacent sequences: A012743 A012744 A012745 * A012747 A012748 A012749

Keyword

nonn

Author

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

Status

approved