OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..250
FORMULA
a(n) = (-1)^n/2*floor(n!*exp(1)-n+1), n>0. - Vladeta Jovovic, Aug 17 2002
E.g.f.: (2+2*x+x^2)/(2*(1+x)*exp(x)) =(1+x/(G(0))/2 ; G(k) = 1 - 1/(1 + x + x^2 - (x*(1+x))^2/(x*(1+x) - (k+1)/(1 + x/G(k+1)))) ; (continued fraction). - Sergei N. Gladkovskii, Dec 28 2011
MATHEMATICA
With[{nmax = 30}, CoefficientList[Series[Cosh[Log[1 + x]]/Exp[x], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jul 28 2018 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+x))/exp(x))) \\ G. C. Greubel, Jul 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+x))/Exp(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 28 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
STATUS
approved