A296731 Expansion of e.g.f. sec(x*cos(x)) (even powers only).

1, 1, -7, -119, 4241, 216241, -16578871, -1851684743, 236706675617, 48609995386849, -8951725537756135, -3042019551814333463, 738962020041708730673, 387782426903449423831441, -116858640965630479825258519, -90328812874963081877073927719

Offset: 0

Author

Ilya Gutkovskiy, Dec 19 2017

Keywords

• sign

Examples

			sec(x*cos(x)) = 1 + x^2/2! - 7*x^4/4! - 119*x^6/6! + 4241*x^8/8! + ...
		

Crossrefs

Cf. A000364, A009008, A009009, A009010, A009011, A009015, A009016, A009446, A009447, A009633, A009634, A102072, A102075, A191512, A296728, A296729, A296730, A296740.

Programs

Mathematica

nmax = 15; Table[(CoefficientList[Series[Sec[x Cos[x]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

PARI

first(n) = x='x+O('x^(2*n-2)); vecextract(Vec(serlaplace(1/cos(x*cos(x)))), (4^n - 1)/3) \\ Iain Fox, Dec 19 2017

Formula

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