A122022 a(n) = a(n-1) - (n-1)*a(n-4), with a(0) = 0, a(1) = 1, a(2) = 2, a(3) = 1.

0, 1, 2, 1, 1, -3, -13, -19, -26, -2, 115, 305, 591, 615, -880, -5150, -14015, -23855, -8895, 83805, 350090, 827190, 1013985, -829725, -8881795, -28734355, -54083980, -32511130, 207297335, 1011859275, 2580294695, 3555628595, -2870588790, -35250085590

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..999 [Offset adapted by Georg Fischer, Jun 06 2021]

Maple

a:= proc(n) option remember;
      if n<3 then n
    elif n=3 then 1
    else a(n-1) - (n-1)*a(n-4)
      fi;
end: seq(a(n), n=0..30); # G. C. Greubel, Oct 06 2019

Mathematica

a[0]=0; a[1]=1; a[2]=2; a[3]=1; a[n_]:= a[n]= a[n-1] - (n-1)*a[n-4]; Table[a[n], {n, 0, 30}]
RecurrenceTable[{a[0]==0, a[1]==1, a[2]==2, a[3]==1, a[n]==a[n-1]- (n-1) a[n-4]}, a, {n, 0, 30}] (* Harvey P. Dale, Nov 28 2014 *)

Prog

(PARI) my(m=30, v=concat([0, 1, 2, 1], vector(m-4))); for(n=5, m, v[n] = v[n-1] - (n-2)*v[n-4]); v \\ G. C. Greubel, Oct 06 2019
(Magma) I:=[0, 1, 2, 1]; [n le 4 select I[n] else Self(n-1) - (n-2)*Self(n-4): n in [1..30]]; // G. C. Greubel, Oct 06 2019
(Sage)
@CachedFunction
def a(n):
    if (n<3): return n
    elif (n==3): return 1
    else: return a(n-1) - (n-1)*a(n-4)
[a(n) for n in (0..30)] # G. C. Greubel, Oct 06 2019
(GAP)
a:= function(n)
    if n<3 then return n;
    elif n=3 then return 1;
    else return a(n-1) - (n-1)*a(n-4);
    fi;
  end;
List([1..30], n-> a(n) ); # G. C. Greubel, Oct 06 2019

Crossrefs

Cf. A000898, A062267, A121966, A122050.

Sequence in context: A212261 A014521 A084389 * A134357 A049258 A228832

Adjacent sequences: A122019 A122020 A122021 * A122023 A122024 A122025

Keyword

sign

Author

Roger L. Bagula, Sep 12 2006

Extensions

Edited by N. J. A. Sloane, Sep 12 2006

Offset corrected by Georg Fischer, Jun 06 2021

Status

approved