A009166 Expansion of cosh(tan(x)*x).

1, 0, 12, 240, 9296, 558720, 47965632, 5537249536, 823842474240, 153119256219648, 34710583399132160, 9416311849673895936, 3009741915237844832256, 1118809461121375449088000

Offset

0,3

Links

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

Formula

a(n) ~ (2*n)! * 2^(2*n-7/4) * exp(2*sqrt(2*n)-1/2) / (n^(3/4) * Pi^(2*n+1/2)). - Vaclav Kotesovec, Jan 24 2015

Mathematica

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

Crossrefs

Sequence in context: A012344 A282789 A012542 * A174556 A012349 A012302

Adjacent sequences: A009163 A009164 A009165 * A009167 A009168 A009169

Keyword

nonn

Author

R. H. Hardin

Extensions

Extended and signs tested Mar 15 1997 by Olivier Gérard.

Status

approved