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

%I A122022 #25 Sep 08 2022 08:45:27
%S A122022 0,1,2,1,1,-3,-13,-19,-26,-2,115,305,591,615,-880,-5150,-14015,-23855,
%T A122022 -8895,83805,350090,827190,1013985,-829725,-8881795,-28734355,
%U A122022 -54083980,-32511130,207297335,1011859275,2580294695,3555628595,-2870588790,-35250085590
%N A122022 a(n) = a(n-1) - (n-1)*a(n-4), with a(0) = 0, a(1) = 1, a(2) = 2, a(3) = 1.
%H A122022 Harvey P. Dale, <a href="/A122022/b122022.txt">Table of n, a(n) for n = 0..999</a> [Offset adapted by _Georg Fischer_, Jun 06 2021]
%p A122022 a:= proc(n) option remember;
%p A122022       if n<3 then n
%p A122022     elif n=3 then 1
%p A122022     else a(n-1) - (n-1)*a(n-4)
%p A122022       fi;
%p A122022 end: seq(a(n), n=0..30); # _G. C. Greubel_, Oct 06 2019
%t A122022 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}]
%t A122022 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 *)
%o A122022 (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
%o A122022 (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
%o A122022 (Sage)
%o A122022 @CachedFunction
%o A122022 def a(n):
%o A122022     if (n<3): return n
%o A122022     elif (n==3): return 1
%o A122022     else: return a(n-1) - (n-1)*a(n-4)
%o A122022 [a(n) for n in (0..30)] # _G. C. Greubel_, Oct 06 2019
%o A122022 (GAP)
%o A122022 a:= function(n)
%o A122022     if n<3 then return n;
%o A122022     elif n=3 then return 1;
%o A122022     else return a(n-1) - (n-1)*a(n-4);
%o A122022     fi;
%o A122022   end;
%o A122022 List([1..30], n-> a(n) ); # _G. C. Greubel_, Oct 06 2019
%Y A122022 Cf. A000898, A062267, A121966, A122050.
%K A122022 sign
%O A122022 0,3
%A A122022 _Roger L. Bagula_, Sep 12 2006
%E A122022 Edited by _N. J. A. Sloane_, Sep 12 2006
%E A122022 Offset corrected by _Georg Fischer_, Jun 06 2021