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 A056889 Numerators of continued fraction for left factorial. 2
 0, 1, 1, 0, 1, -1, -2, 1, 2, -1, -3, 2, 9, -7, -40, 33, 224, -191, -1495, 1304, 11545, -10241, -101106, 90865, 989274, -898409, -10690043, 9791634, 126392833, -116601199, -1622625152, 1506023953, 22473758096, -20967734143, -333977722335, 313009988192, 5300202065121, -4987192076929 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS G. C. Greubel, Table of n, a(n) for n = 0..900 FORMULA a(0) = 0; 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). From Mark van Hoeij, Jul 15 2022: (Start) a(2*n+1) = -(-1)^n * A058797(n-2). a(2*n) = (-1)^n * (A058797(n-2) + A058797(n-3)). (End) MAPLE a:= proc(n) option remember; if n<2 then 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, 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, 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 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 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. A056890, A058797. Sequence in context: A029198 A029175 A186994 * A275761 A232396 A270096 Adjacent sequences: A056886 A056887 A056888 * A056890 A056891 A056892 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

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Last modified December 3 08:35 EST 2022. Contains 358515 sequences. (Running on oeis4.)