A296791 Expansion of e.g.f. sech(x*sec(x)) (even powers only).

1, -1, -7, -1, 3121, 132959, -1261591, -889217057, -79029091743, 5889540654911, 3289057601679065, 395957721046153023, -120519140613246313327, -71865162873642033099361, -9267049529998625177827639, 8376363338336819515365004319, 5693280488360087435524724806849

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

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

Example

sech(x*sec(x)) = 1 - x^2/2! - 7*x^4/4! - x^6/6! + 3121*x^8/8! + ...

Mathematica

nmax = 16; Table[(CoefficientList[Series[Sech[x Sec[x]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

Crossrefs

Cf. A000364, A003721, A003722, A009008, A009009, A009010, A009011, A009015, A009016, A009118, A009562, A009765, A102072, A102075, A296731, A296740, A296790.

Sequence in context: A357389 A245329 A309171 * A246851 A258763 A258753

Adjacent sequences: A296788 A296789 A296790 * A296792 A296793 A296794

Keyword

sign

Author

Ilya Gutkovskiy, Dec 20 2017

Status

approved