A296790 Expansion of e.g.f. sec(x*sec(x)) (even powers only).

1, 1, 17, 601, 38849, 4022641, 609933521, 127391254537, 35067716300033, 12304447787106529, 5360597104269331985, 2839145693984474128057, 1796556232541725248396737, 1338623568393194541863879761, 1160057210771530210422755155409, 1156898060700987368136296212581481

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..220

Formula

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

a(n) ~ c * d^n * n^(2*n + 1/2) / exp(2*n), where d = 4.5851486299312178337601256220116584724159... is the real root of the equation sqrt(d) * cos(2/sqrt(d)) = 4/Pi and c = 1.99453594228967461336... - Vaclav Kotesovec, Dec 21 2017

Example

sec(x*sec(x)) = 1 + x^2/2! + 17*x^4/4! + 601*x^6/6! + 38849*x^8/8! + ...

Mathematica

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

Crossrefs

Cf. A000364, A003712, A003718, A009008, A009009, A009010, A009011, A009015, A009118, A009562, A009765, A102072, A102075, A296731, A296740, A296791.

Sequence in context: A202407 A009709 A162490 * A330516 A142744 A219090

Adjacent sequences: A296787 A296788 A296789 * A296791 A296792 A296793

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 20 2017

Status

approved