A009291 Expansion of exp(x)/cos(tan(x)).

1, 1, 2, 4, 20, 76, 608, 3256, 34320, 235408, 3084640, 25823744, 405224896, 4007103296, 73292662784, 836059707008, 17468683774208, 225808591264000, 5306511481924096, 76659294873275392, 2001393333656871936

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(n) ~ n! * 4 * ((-1)^n + exp(2*arctan(Pi/2))) / ((4 + Pi^2) * exp(arctan(Pi/2)) * arctan(Pi/2)^(n+1)). - Vaclav Kotesovec, Jan 23 2015

Mathematica

Exp[ x ]/Cos[ Tan[ x ] ]
CoefficientList[Series[E^x*Sec[Tan[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)

Crossrefs

Sequence in context: A286344 A279153 A204550 * A081440 A204438 A325791

Adjacent sequences: A009288 A009289 A009290 * A009292 A009293 A009294

Keyword

nonn,easy

Author

R. H. Hardin

Extensions

Extended and signs tested Mar 15 1997 by Olivier Gérard.

Status

approved