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%I #29 Jul 21 2018 20:26:28
%S 1,1,13,397,22265,1996569,262056837,47378857957,11289999097969,
%T 3429209143916337,1293273763150662781,592937704157794933821,
%U 324791587492604492427881,209490216975221386279672393,157153880464155360205476452597
%N Expansion of e.g.f.: 1/cos(tan(x)) (even-indexed coefficients only).
%H G. C. Greubel, <a href="/A009010/b009010.txt">Table of n, a(n) for n = 0..200</a> (terms 0..50 from Vincenzo Librandi)
%F a(n) ~ (2*n)! * 8 / ((4+Pi^2) * (arctan(Pi/2))^(2*n+1)). - _Vaclav Kotesovec_, Jan 22 2015
%t f[x_] := Sec@Tan[x]; Table[Derivative[2*n][f][0], {n, 0, 14}] (* _Arkadiusz Wesolowski_, Aug 18 2012 *)
%t 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 *)
%o (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
%K nonn
%O 0,3
%A _R. H. Hardin_
%E Extended and signs tested by _Olivier Gérard_, Mar 15 1997
%E a(14) from _Arkadiusz Wesolowski_, Aug 18 2012
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