A012616 arcsinh(arcsinh(x)*tan(x))=2/2!*x^2+4/4!*x^4-10/6!*x^6-2872/8!*x^8...

0, 2, 4, -10, -2872, 83818, 10194380, 1201034718, -434124645744, -21017961579822, 3112138256976532, 12699119070248719814, -2651876213664722621096, -900449010135889648937414

Offset

0,2

Links

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

Formula

a(n) ~ (-1)^(n+1) * 2^(2*n+1) * n^(2*n-1) * sinh(1) / (exp(2*n) * sqrt(Pi^2*cosh(1)^2-Pi^2+4*cosh(1)^2)). - Vaclav Kotesovec, Oct 31 2013

Mathematica

Table[n!*SeriesCoefficient[ArcSinh[ArcSinh[x]*Tan[x]], {x, 0, n}], {n, 0, 40, 2}] (* Vaclav Kotesovec, Oct 31 2013 *)

Crossrefs

Sequence in context: A327059 A012555 A012722 * A012611 A356109 A356175

Adjacent sequences: A012613 A012614 A012615 * A012617 A012618 A012619

Keyword

sign

Author

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

Extensions

Prepended missing a(0)=0 from Vaclav Kotesovec, Oct 31 2013

Status

approved