A056890 Denominators of continued fraction for left factorial.

1, -1, 0, -1, -2, 1, 1, 0, 1, -1, -4, 3, 14, -11, -63, 52, 353, -301, -2356, 2055, 18194, -16139, -159335, 143196, 1559017, -1415821, -16846656, 15430835, 199185034, -183754199, -2557127951, 2373373752, 35416852081, -33043478329, -526322279512, 493278801183, 8352696141782

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..900

Formula

a(0)=1; a(1)=-1; a(2*n)=n*a(2*n-1)+a(2*n-2); a(2*n+1)= - a(2*n)+a(2*n-1)

Maple

a:= proc(n) option remember;
      if n<2 then (-1)^n
    elif (n mod 2)=0 then (n/2)*a(n-1) +a(n-2)
    else -a(n-1) +a(n-2)
      fi; end:
seq(a(n), n=0..40); # G. C. Greubel, Dec 05 2019

Mathematica

a[n_]:= a[n]= If[n<2, (-1)^n, If[EvenQ[n], (n/2)*a[n-1] +a[n-2], -a[n-1] +a[n-2]]]; Table[a[n], {n, 0, 40}] (* G. C. Greubel, Dec 05 2019 *)

Prog

(PARI) a(n) = if(n<2, (-1)^n, if(Mod(n, 2)==0, (n/2)*a(n-1) +a(n-2), -a(n-1) +a(n-2) )); \\ G. C. Greubel, Dec 05 2019
(Sage)
@CachedFunction
def a(n):
    if (n<2): return (-1)^n
    elif (mod(n, 2) ==0): return (n/2)*a(n-1) +a(n-2)
    else: return -a(n-1) +a(n-2)
[a(n) for n in (0..40)] # G. C. Greubel, Dec 05 2019
(GAP)
a:= function(n)
    if n<2 then return (-1)^n;
    elif (n mod 2)=0 then return (n/2)*a(n-1) +a(n-2);
    else return -a(n-1) +a(n-2);
    fi; end;
List([0..20], n-> a(n) ); # G. C. Greubel, Dec 05 2019

Crossrefs

Cf. A056889.

Sequence in context: A294446 A318163 A114640 * A321519 A346392 A169590

Adjacent sequences: A056887 A056888 A056889 * A056891 A056892 A056893

Keyword

sign,frac,easy

Author

Aleksandar Petojevic, Sep 05 2000

Extensions

More terms from James A. Sellers, Sep 06 2000 and from Larry Reeves (larryr(AT)acm.org), Sep 07 2000

Status

approved