A012664 arcsinh(tanh(x)*sin(x))=2/2!*x^2-12/4!*x^4+22/6!*x^6+6888/8!*x^8...

0, 2, -12, 22, 6888, -422998, -19858212, 10668149182, -1244673483312, -393680785867438, 254550574752219588, -30031176795810056858, -50358282178393089181512, 38448631613848702263196922

Offset

0,2

Links

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

Formula

Lim sup n->infinity (|a(n)|/(2*n)!)^(1/(2*n)) = 1.0688665046968199... = abs(1/r), where r is the complex root of the equation sin(r)*exp(2*r) - sin(r) + I*exp(2*r) = -I. - Vaclav Kotesovec, Nov 02 2013

Mathematica

Table[n!*SeriesCoefficient[ArcSinh[Tanh[x]*Sin[x]], {x, 0, n}], {n, 0, 40, 2}] (* Vaclav Kotesovec, Nov 02 2013 *)

Crossrefs

Sequence in context: A233137 A094626 A093378 * A012545 A009514 A192851

Adjacent sequences: A012661 A012662 A012663 * A012665 A012666 A012667

Keyword

sign

Author

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

Extensions

Prepended missing a(0)=0 from Vaclav Kotesovec, Nov 02 2013

Status

approved