A009109 Expansion of e.g.f. cos(x)/cosh(sin(x)), even powers only.

1, -2, 16, -328, 12160, -721280, 62638720, -7495723264, 1182630301696, -237887012458496, 59422015832915968, -18045969534514167808, 6548012482760106213376, -2797775464269494922051584

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..232

Formula

a(n) ~ (2*n)! * 2 * (-1)^n / (log((Pi+sqrt(4+Pi^2))/2))^(2*n+1). - Vaclav Kotesovec, Jan 22 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Cos[x]*Sech[Sin[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Jan 22 2015 *)

Prog

(PARI) x='x+O('x^50); v=Vec(serlaplace(cos(x)/cosh(sin(x)))); vector(#v\2, n, v[2*n-1]) \\ G. C. Greubel, Jul 26 2018

Crossrefs

Sequence in context: A336522 A294039 A009100 * A268560 A275854 A299907

Adjacent sequences: A009106 A009107 A009108 * A009110 A009111 A009112

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved