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%I #16 Jul 26 2018 08:04:37
%S 1,0,4,56,2192,128448,11141824,1332816512,210250492160,42290401757184,
%T 10563624419906560,3208072210301966336,1164053448822395604992,
%U 497366043438147538010112,247165485059674632625438720
%N Expansion of e.g.f. cos(x)/cos(sinh(x)), even powers only.
%H G. C. Greubel, <a href="/A009105/b009105.txt">Table of n, a(n) for n = 0..232</a>
%F a(n) ~ (2*n)! * 4 * cos(arcsinh(Pi/2)) / (sqrt(4+Pi^2) * arcsinh(Pi/2)^(2*n+1)). - _Vaclav Kotesovec_, Jan 22 2015
%t nn = 20; Table[(CoefficientList[Series[Cos[x]*Sec[Sinh[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(cos(x)/cos(sinh(x)))); vector(#v\2,n,v[2*n-1]) \\ _G. C. Greubel_, Jul 26 2018
%K nonn
%O 0,3
%A _R. H. Hardin_
%E Extended and signs tested by _Olivier Gérard_, Mar 15 1997