A012843 tan(sec(x)*arctanh(x))=x+7/3!*x^3+185/5!*x^5+11471/7!*x^7...

1, 7, 185, 11471, 1263185, 215079159, 52220520521, 17117211436287, 7278847910698529, 3895256097472909671, 2561265786122546675545, 2029572906879775183011503, 1907361016227301624675795825

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/(1-r^2) + Pi*sin(r)) * r^(2*n+2)), where r = 0.7989151684962902269091787502961348455829847186615330217492... is the root of the equation sec(r)*arctanh(r) = Pi/2. - Vaclav Kotesovec, Feb 07 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[ArcTanh[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: A217244 A152436 A176338 * A012798 A297765 A193811

Adjacent sequences: A012840 A012841 A012842 * A012844 A012845 A012846

Keyword

nonn

Author

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

Status

approved