A012536 tan(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, 1429888, 189299200, 34859305728, 8524943044608, 2667935751684096, 1040196824976736256, 494214397360327786496, 281064144909266002903040, 188495115535527543004266496

Offset

0,2

Links

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

Formula

a(n) ~ 4 * (2*n)! / ((Pi/tanh(r) + 2*sinh(r)/sqrt(1-r^2)) * r^(2*n+1)), where r = 0.980280472307130556844984772871395757744942110943939753792691... is the root of the equation sinh(r)*arcsin(r) = Pi/2. - Vaclav Kotesovec, Feb 06 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[ArcSin[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: A012913 A217728 A013086 * A012541 A054943 A013135

Adjacent sequences: A012533 A012534 A012535 * A012537 A012538 A012539

Keyword

nonn

Author

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

Extensions

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

Status

approved