A012751 tan(arctanh(x)*sinh(x))=2/2!*x^2+12/4!*x^4+430/6!*x^6+27384/8!*x^8...

0, 2, 12, 430, 27384, 2844538, 444855620, 96566466022, 27798112443248, 10239758940342642, 4695120560496345596, 2621628020059813754526, 1751011006876497963996520, 1378272807335260827405511146

Offset

0,2

Links

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

Formula

a(n) ~ 4*(1-r^2) * (2*n)! / (((1-r^2)*Pi/tanh(r) + 2*sinh(r)) * r^(2*n+1)), where r = 0.907648090497239832680442727614114269985280667634413195506087... is the root of the equation arctanh(r)*sinh(r) = Pi/2. - Vaclav Kotesovec, Feb 06 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[ArcTanh[x]*Sinh[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 06 2015 *)

Crossrefs

Sequence in context: A015181 A012378 A012383 * A012428 A012786 A168504

Adjacent sequences: A012748 A012749 A012750 * A012752 A012753 A012754

Keyword

nonn

Author

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

Extensions

a(0)=0 prepended by Vaclav Kotesovec, Feb 06 2015

Status

approved