A009106 Expansion of e.g.f. cos(x)/cos(tan(x)), even powers only.

1, 0, 8, 216, 12032, 1075328, 140944000, 25464568832, 6065774456832, 1842040163078144, 694620312112857088, 318448731218429771776, 174429761567957718302720, 112504917152076237383401472

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..224

Formula

a(n) ~ (2*n)! * 16 / ((4+Pi^2)^(3/2) * arctan(Pi/2)^(2*n+1)). - Vaclav Kotesovec, Jan 22 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Cos[x]*Sec[Tan[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Jan 22 2015 *)

Prog

(PARI) x='x+O('x^50); v=Vec(serlaplace(cos(x)/cos(tan(x)))); vector(#v\2, n, v[2*n-1]) \\ G. C. Greubel, Jul 26 2018

Crossrefs

Sequence in context: A009072 A002897 A024289 * A000442 A268471 A342598

Adjacent sequences: A009103 A009104 A009105 * A009107 A009108 A009109

Keyword

nonn

Author

R. H. Hardin

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

Status

approved