A012618 arctanh(arcsinh(x)*tan(x))=2/2!*x^2+4/4!*x^4+350/6!*x^6+7208/8!*x^8...

0, 2, 4, 350, 7208, 1520218, 106485740, 38051376246, 6123846322896, 3217389043510578, 964215477538459732, 692917532440212444686, 338776184246581290006520, 318786053587029917056642186

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

a(n) ~ (2*n-1)! / r^(2*n), where r = 0.89357177742189289... is the root of the equation r+sqrt(r^2+1) = exp(1/tan(r)). - Vaclav Kotesovec, Oct 31 2013

Mathematica

Table[n!*SeriesCoefficient[ArcTanh[ArcSinh[x]*Tan[x]], {x, 0, n}], {n, 0, 40, 2}] (* Vaclav Kotesovec, Oct 31 2013 *)

Crossrefs

Sequence in context: A009705 A012372 A012613 * A012557 A012562 A263959

Adjacent sequences: A012615 A012616 A012617 * A012619 A012620 A012621

Keyword

nonn

Author

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

Extensions

Prepended missing a(0)=0 from Vaclav Kotesovec, Oct 31 2013

Status

approved