A009010 Expansion of e.g.f.: 1/cos(tan(x)) (even-indexed coefficients only).

1, 1, 13, 397, 22265, 1996569, 262056837, 47378857957, 11289999097969, 3429209143916337, 1293273763150662781, 592937704157794933821, 324791587492604492427881, 209490216975221386279672393, 157153880464155360205476452597

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..200 (terms 0..50 from Vincenzo Librandi)

Programs

Mathematica

f[x_] := Sec@Tan[x]; Table[Derivative[2*n][f][0], {n, 0, 14}] (* Arkadiusz Wesolowski, Aug 18 2012 *)
nn = 20; Table[(CoefficientList[Series[Sec[Tan[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Jan 22 2015 *)

PARI

x='x+O('x^50); v=Vec(serlaplace(1/cos(tan(x)))); vector(#v\2,n,v[2*n-1]) \\ G. C. Greubel, Jul 21 2018

Formula

a(n) ~ (2*n)! * 8 / ((4+Pi^2) * (arctan(Pi/2))^(2*n+1)). - Vaclav Kotesovec, Jan 22 2015

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

a(14) from Arkadiusz Wesolowski, Aug 18 2012