A009114 Expansion of e.g.f. cos(x)/exp(tan(x)).

1, -1, 0, 0, 4, -12, 56, -280, 1744, -11536, 86208, -703296, 6199744, -59653440, 608357504, -6715007104, 77889982720, -967972497664, 12588540708864, -173764741920768, 2503565961032704, -37986612815698944

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

Formula

a(n) ~ n! * (-1)^n * 2^(n-5/4) * exp((1 + 2*sqrt(2*Pi*n))/Pi) / (n^(5/4) * Pi^(n+1/4)). - Vaclav Kotesovec, Jan 24 2015

Mathematica

CoefficientList[Series[Cos[x]/E^Tan[x], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(cos(x)/exp(tan(x)))) \\ G. C. Greubel, Jul 26 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(x)/Exp(Tan(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 26 2018

Crossrefs

Sequence in context: A124004 A243785 A019266 * A144012 A197924 A065125

Adjacent sequences: A009111 A009112 A009113 * A009115 A009116 A009117

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved