A012753 tan(arctanh(x)*arcsinh(x))=2/2!*x^2+4/4!*x^4+398/6!*x^6+10344/8!*x^8...

0, 2, 4, 398, 10344, 1808442, 161718060, 45246852870, 8895239749200, 3696108480038130, 1280274899653919700, 747254995555318476030, 400947704397371982315960, 314940075899759001168711210

Offset

0,2

Links

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

Formula

a(n) ~ 4 * (2*n)! / ((Pi / (arcsinh(r)*sqrt(1+r^2)) + 2*arcsinh(r) / (1-r^2)) * r^(2*n+1)), where r = 0.9521457236040528180035996172241256876113834258238... is the root of the equation arctanh(r)*arcsinh(r) = Pi/2. - Vaclav Kotesovec, Feb 06 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[ArcSinh[x]*ArcTanh[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: A263959 A216024 A247220 * A012440 A058172 A122808

Adjacent sequences: A012750 A012751 A012752 * A012754 A012755 A012756

Keyword

nonn

Author

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

Extensions

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

Status

approved