A012378 tan(tan(x)*arcsin(x))=2/2!*x^2+12/4!*x^4+430/6!*x^6+26040/8!*x^8...

0, 2, 12, 430, 26040, 2661178, 402231940, 84456360742, 23476965450736, 8341678414816242, 3686586514781799292, 1982979948714026781726, 1275341677617693817452200, 966341800352400737116306986

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..220

Formula

a(n) ~ 2 * (2*n)! / ((Pi/sin(2*r) + tan(r)/sqrt(1-r^2)) * r^(2*n+1)), where r = 0.925530521691094119047741289850... is the root of the equation tan(r)*arcsin(r) = Pi/2. - Vaclav Kotesovec, Feb 06 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[ArcSin[x]*Tan[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: A072446 A220113 A015181 * A012383 A012751 A012428

Adjacent sequences: A012375 A012376 A012377 * A012379 A012380 A012381

Keyword

nonn

Author

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

Extensions

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

Status

approved