A009841 Expansion of tanh(x)/cos(tan(x)) (odd powers only).

1, 1, 61, 1933, 158041, 16465241, 2606419349, 539107003685, 146079106941745, 49518212296709809, 20652025953651072109, 10367691465318376289725, 6173444725835144560476041, 4300227332637862306820286985

Offset

1,3

Links

Table of n, a(n) for n=1..14.

Formula

a(n) ~ (2*n-1)! * 8 * tanh(arctan(Pi/2)) / ((4 + Pi^2) * arctan(Pi/2)^(2*n)). - Vaclav Kotesovec, Jan 24 2015

Mathematica

Tanh[ x ]/Cos[ Tan[ x ] ] (* Odd Part *)
nn = 20; Table[(CoefficientList[Series[Sec[Tan[x]]*Tanh[x], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Jan 24 2015 *)

Crossrefs

Sequence in context: A017777 A113054 A017724 * A038650 A224441 A078962

Adjacent sequences: A009838 A009839 A009840 * A009842 A009843 A009844

Keyword

nonn

Author

R. H. Hardin

Extensions

Extended and signs tested Mar 15 1997 by Olivier Gérard.

Changed offset by Vaclav Kotesovec, Jan 24 2015

Status

approved