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A122021 a(n) = a(n-2) - (n-1)*a(n-3), with a(0) = 0, a(1) = 1, a(2) = 2.

%I A122021 #14 Sep 08 2022 08:45:27
%S A122021 0,1,2,1,-1,-7,-6,-1,43,47,52,-383,-465,-1007,4514,5503,19619,-66721,
%T A122021 -73932,-419863,1193767,1058777,10010890,-25204097,-14340981,
%U A122021 -265465457,615761444,107400049,7783328783,-17133920383,4668727362
%N A122021 a(n) = a(n-2) - (n-1)*a(n-3), with a(0) = 0, a(1) = 1, a(2) = 2.
%H A122021 G. C. Greubel, <a href="/A122021/b122021.txt">Table of n, a(n) for n = 0..1000</a>
%p A122021 a:= proc(n) option remember;
%p A122021 if n < 3 then n
%p A122021 else a(n-2)-(n-1)*a(n-3)
%p A122021 fi;
%p A122021 end proc;
%p A122021 seq(a(n), n = 0..30); # _G. C. Greubel_, Oct 06 2019
%t A122021 a[0]=0; a[1]=1; a[2]=2; a[n_]:= a[n]= a[n-2] - (n-1)*a[n-3]; Table[a[n], {n, 0, 30}]
%t A122021 RecurrenceTable[{a[0]==0,a[1]==1,a[2]==2,a[n]==a[n-2]-(n-1)a[n-3]},a,{n,30}] (* _Harvey P. Dale_, Apr 29 2022 *)
%o A122021 (PARI) my(m=30, v=concat([0,1,2], vector(m-3))); for(n=4, m, v[n] = v[n-2] - (n-2)*v[n-3]); v \\ _G. C. Greubel_, Oct 06 2019
%o A122021 (Magma) I:=[0,1,2]; [n le 3 select I[n] else Self(n-2) - (n-2)*Self(n-3): n in [1..30]]; // _G. C. Greubel_, Oct 06 2019
%o A122021 (Sage)
%o A122021 def a(n):
%o A122021     if (n<3): return n
%o A122021     else: return a(n-2) - (n-1)* a(n-3)
%o A122021 [a(n) for n in (0..30)] # _G. C. Greubel_, Oct 06 2019
%o A122021 (GAP)
%o A122021 a:= function(n)
%o A122021     if n<3 then return n;
%o A122021     else return a(n-2) - (n-1)*a(n-3);
%o A122021     fi;
%o A122021   end;
%o A122021 List([0..30], n-> a(n) ); # _G. C. Greubel_, Oct 06 2019
%Y A122021 Cf. A000898, A121966, A062267.
%K A122021 sign
%O A122021 0,3
%A A122021 _Roger L. Bagula_, Sep 12 2006
%E A122021 Edited by _N. J. A. Sloane_, Sep 12 2006
%E A122021 Offset changed by _G. C. Greubel_, Oct 06 2019