A296939 Expansion of e.g.f. sec(x*tan(x/2)) (even powers only).

1, 0, 3, 15, 644, 17145, 1124673, 74115496, 7730031915, 921044459943, 145334164141820, 26830525240048761, 6053646614467427553, 1586816790903080698000, 487642998132913180824819, 171640559783810345998524735, 69078935661419038650738789428

Offset: 0

Author

Ilya Gutkovskiy, Dec 22 2017

Keywords

• nonn

Examples

			sec(x*tan(x/2)) = 1 + 3*x^4/4! + 15*x^6/6! + 644*x^8/8! + ...
		

Crossrefs

Cf. A000364, A001469, A009010, A110501, A296839, A296841, A296842, A296853, A296854, A296856, A296940.

Programs

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}]

Formula

a(n) = (2*n)! * [x^(2*n)] sec(x*tan(x/2)).