A013087 tan(arcsinh(x)+arcsin(x))=2*x+16/3!*x^3+530/5!*x^5+37840/7!*x^7...

2, 16, 530, 37840, 4665890, 880829200, 236051798450, 85184059714000, 39823482623005250, 23410203659063338000, 16900988192636551591250, 14700311020824054699970000, 15161633552176216519055281250

Offset

0,1

Links

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

Formula

a(n) ~ 2 * sqrt(1-r^4) * (2*n+1)! / ((sqrt(1-r^2) + sqrt(1+r^2)) * r^(2*n+2)), where r = 0.762718149449013683089118440018621705719487630300437769993... is the root of the equation arcsinh(r) + arcsin(r) = Pi/2. - Vaclav Kotesovec, Feb 07 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[ArcSin[x] + ArcSinh[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 07 2015 *)

Crossrefs

Sequence in context: A012919 A012914 A168404 * A121271 A013136 A013004

Adjacent sequences: A013084 A013085 A013086 * A013088 A013089 A013090

Keyword

nonn

Author

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

Status

approved