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A056920 Denominators of continued fraction for left factorial.

%I A056920 #12 Jul 02 2025 16:02:00
%S A056920 1,1,0,-1,-1,1,4,1,-15,-19,56,151,-185,-1091,204,7841,6209,-56519,
%T A056920 -112400,396271,1520271,-2442439,-19165420,7701409,237686449,
%U A056920 145269541,-2944654296,-4833158329,36392001815,104056218421,-441823808804,-2002667085119,5066513855745,37109187217649
%N A056920 Denominators of continued fraction for left factorial.
%H A056920 G. C. Greubel, <a href="/A056920/b056920.txt">Table of n, a(n) for n = 0..895</a>
%F A056920 a(0)=1, a(1)=1, a(n) = a(n-1) - floor(n/2)*a(n-2).
%p A056920 a:= proc(n) option remember;
%p A056920    if n<2 then 1
%p A056920    else a(n-1) - floor(n/2)*a(n-2)
%p A056920    fi; end:
%p A056920 seq(a(n), n=0..40); # _G. C. Greubel_, Dec 05 2019
%t A056920 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 *)
%o A056920 (PARI) a(n) = if(n<2, n, a(n-1) - (n\2)*a(n-2) ); \\ _G. C. Greubel_, Dec 05 2019
%o A056920 (Magma)
%o A056920 function a(n)
%o A056920   if n lt 2 then return 1;
%o A056920   else return a(n-1) - Floor(n/2)*a(n-2);
%o A056920   end if; return a; end function;
%o A056920 [a(n): n in [0..40]]; // _G. C. Greubel_, Dec 05 2019
%o A056920 (Sage)
%o A056920 @CachedFunction
%o A056920 def a(n):
%o A056920     if (n<2): return 1
%o A056920     else: return a(n-1) - floor(n/2)*a(n-2)
%o A056920 [a(n) for n in (0..40)] # _G. C. Greubel_, Dec 05 2019
%o A056920 (GAP)
%o A056920 a:= function(n)
%o A056920     if n<2 then return 1;
%o A056920     else return a(n-1) - Int(n/2)*a(n-2);
%o A056920     fi; end;
%o A056920 List([0..40], n-> a(n) ); # _G. C. Greubel_, Dec 05 2019
%K A056920 sign,frac,easy
%O A056920 0,7
%A A056920 _Aleksandar Petojevic_, Sep 05 2000
%E A056920 More terms from _James Sellers_, Sep 06 2000