A012363 arctanh(tan(x)*exp(x))=x+2/2!*x^2+7/3!*x^3+36/4!*x^4+285/5!*x^5...

0, 1, 2, 7, 36, 285, 2662, 30147, 395976, 5968505, 101054282, 1901962687, 39368308716, 889051951125, 21749632880302, 573017429752827, 16174993678778256, 487024011982108145, 15580632579831576722

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) ~ (n-1)!/(2*r^n), where r = 0.5313908566521572... is the root of the equation tan(r)*exp(r)=1. - Vaclav Kotesovec, Oct 24 2013

Mathematica

CoefficientList[Series[ArcTanh[Tan[x]*Exp[x]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 24 2013 *)

Crossrefs

Sequence in context: A141308 A185161 A012712 * A012717 A072236 A007474

Adjacent sequences: A012360 A012361 A012362 * A012364 A012365 A012366

Keyword

nonn

Author

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

Extensions

Prepended missing a(0)=0, Vaclav Kotesovec, Oct 24 2013

Status

approved