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%I #5 Dec 22 2017 09:01:01
%S 1,0,3,15,644,17145,1124673,74115496,7730031915,921044459943,
%T 145334164141820,26830525240048761,6053646614467427553,
%U 1586816790903080698000,487642998132913180824819,171640559783810345998524735,69078935661419038650738789428
%N Expansion of e.g.f. sec(x*tan(x/2)) (even powers only).
%F a(n) = (2*n)! * [x^(2*n)] sec(x*tan(x/2)).
%e sec(x*tan(x/2)) = 1 + 3*x^4/4! + 15*x^6/6! + 644*x^8/8! + ...
%t nmax = 16; Table[(CoefficientList[Series[Sec[x Tan[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
%Y Cf. A000364, A001469, A009010, A110501, A296839, A296841, A296842, A296853, A296854, A296856, A296940.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 22 2017
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