A012824 tan(sec(x)*arcsinh(x))=x+4/3!*x^3+80/5!*x^5+3176/7!*x^7+240128/9!*x^9...

1, 4, 80, 3176, 240128, 26523264, 4329123968, 926411177472, 262606340440064, 92031599216406528, 40177149524079247360, 20888461815920151461888, 13005071730835628127846400, 9394925108531366128729587712

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Vaclav Kotesovec, Graph - abs(e.g.f.) in the complex plane

Formula

a(n) ~ 4 * cos(r) * (2*n+1)! / ((2/sqrt(1+r^2) + Pi*sin(r)) * r^(2*n+2)), where r = 0.9838660479616109267190065546103701708288146085255331828633... is the root of the equation sec(r)*arcsinh(r) = Pi/2. - Vaclav Kotesovec, Feb 07 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[ArcSinh[x]*Sec[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 07 2015 *)

Crossrefs

Sequence in context: A057875 A187543 A268734 * A012057 A214298 A102063

Adjacent sequences: A012821 A012822 A012823 * A012825 A012826 A012827

Keyword

nonn

Author

Patrick Demichel

Status

approved