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A296939
Expansion of e.g.f. sec(x*tan(x/2)) (even powers only).
3
1, 0, 3, 15, 644, 17145, 1124673, 74115496, 7730031915, 921044459943, 145334164141820, 26830525240048761, 6053646614467427553, 1586816790903080698000, 487642998132913180824819, 171640559783810345998524735, 69078935661419038650738789428
OFFSET
0,3
FORMULA
a(n) = (2*n)! * [x^(2*n)] sec(x*tan(x/2)).
EXAMPLE
sec(x*tan(x/2)) = 1 + 3*x^4/4! + 15*x^6/6! + 644*x^8/8! + ...
MATHEMATICA
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}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 22 2017
STATUS
approved