A012541 arctanh(sinh(x)*arcsin(x))=2/2!*x^2+8/4!*x^4+320/6!*x^6+15808/8!*x^8...

0, 2, 8, 320, 15808, 1671808, 242521600, 52294963968, 14823920529408, 5496196568825856, 2548323017071149056, 1453790822661022908416, 997862723859007908085760, 812410035086507459409412096

Offset

0,2

Links

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

Formula

a(n) ~ (2*n-1)! / r^(2*n), where r = 0.858737427017558097934130835838437454788... is the root of the equation sinh(r)*arcsin(r) = 1. - Vaclav Kotesovec, Feb 05 2015

Mathematica

With[{nn=30}, Flatten[{0, Take[CoefficientList[Series[ArcTanh[Sinh[x]ArcSin[x]], {x, 0, nn}], x] Range[0, nn]!, {3, -1, 2}]}]] (* Harvey P. Dale, Oct 31 2013 *)

Crossrefs

Sequence in context: A217728 A013086 A012536 * A054943 A013135 A012999

Adjacent sequences: A012538 A012539 A012540 * A012542 A012543 A012544

Keyword

nonn

Author

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

Extensions

Prepended missing a(0)=0 from Vaclav Kotesovec, Feb 05 2015

Status

approved