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

Author

Roger L. Bagula, Sep 12 2006

Keywords

• sign

Links

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

Crossrefs

Cf. A000898, A062267, A121966, A122050.

Programs

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

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

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 *)

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

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

Extensions

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

Offset corrected by Georg Fischer, Jun 06 2021