A056920 Denominators of continued fraction for left factorial.

1, 1, 0, -1, -1, 1, 4, 1, -15, -19, 56, 151, -185, -1091, 204, 7841, 6209, -56519, -112400, 396271, 1520271, -2442439, -19165420, 7701409, 237686449, 145269541, -2944654296, -4833158329, 36392001815, 104056218421, -441823808804, -2002667085119, 5066513855745, 37109187217649

Offset: 0

Author

Aleksandar Petojevic, Sep 05 2000

Keywords

• sign
• frac
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..895

Programs

GAP

a:= function(n)
    if n<2 then return 1;
    else return a(n-1) - Int(n/2)*a(n-2);
    fi; end;
List([0..40], n-> a(n) ); # G. C. Greubel, Dec 05 2019

Magma

function a(n)
  if n lt 2 then return 1;
  else return a(n-1) - Floor(n/2)*a(n-2);
  end if; return a; end function;
[a(n): n in [0..40]]; // G. C. Greubel, Dec 05 2019

Maple

a:= proc(n) option remember;
   if n<2 then 1
   else a(n-1) - floor(n/2)*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, a[n-1] -Floor[n/2]*a[n-2]]; Table[a[n], {n,0,40}] (* G. C. Greubel, Dec 05 2019 *)

PARI

a(n) = if(n<2, n, a(n-1) - (n\2)*a(n-2) ); \\ G. C. Greubel, Dec 05 2019

Sage

@CachedFunction
def a(n):
    if (n<2): return 1
    else: return a(n-1) - floor(n/2)*a(n-2)
[a(n) for n in (0..40)] # G. C. Greubel, Dec 05 2019

Formula

a(0)=1, a(1)=1, a(n) = a(n-1) - floor(n/2)*a(n-2).

Extensions

More terms from James Sellers, Sep 06 2000