A122092 - OEIS

%I #9 Apr 02 2023 16:29:11

%S 1,1,-1,-3,-3,3,27,117,513,2655,16623,123057,1047717,10048203,

%T 106958115,1249780653,15892557417,218391870807,3224096456823,

%U 50878586091465,854556716966733,15219005900538627,286434426954471147,5680304836232044293,118378714577152138065

%N a(n) = (n-2)*a(n-1) - (n-1)*a(n-2), with a(0)=1, a(1)=1.

%H G. C. Greubel, <a href="/A122092/b122092.txt">Table of n, a(n) for n = 0..350</a>

%p a:= proc(n) option remember;

%p if n<2 then 1

%p elif n = 2 then -1

%p else (n-2)*a(n-1)-(n-1)*a(n-2)

%p end if; end proc;

%p seq(a(n), n = 0 .. 25); # _G. C. Greubel_, Oct 02 2019

%t a[0]=1;a[1]=1;a[n_]:=a[n]=(n-2)a[n-1]-(n-1)a[n-2]; Table[a[n],{n,0,20}]

%t nxt[{n_,a_,b_}]:={(n+1),b,b(n-1)-a n}; NestList[nxt,{1,1,1},30][[;;,2]] (* _Harvey P. Dale_, Apr 02 2023 *)

%o (PARI) a(n) = if(n==0 || n==1, 1, (n-2)*a(n-1) - (n-1)*a(n-2));

%o vector(26, n, a(n-1)) \\ _G. C. Greubel_, Oct 02 2019

%o (Magma) I:=[1,1,-1]; [n le 3 select I[n] else (n-3)*Self(n-1) - (n-2)*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Oct 02 2019

%o (Sage)

%o def a(n):

%o     if (n<2): return 1

%o     elif (n==2): return -1

%o     else: return (n-2)*a(n-1) - (n-1)*a(n-2)

%o [a(n) for n in (0..25)] # _G. C. Greubel_, Oct 02 2019

%o (GAP) a:=[1,1,-1];; for n in [4..25] do a[n]:=(n-3)*a[n-1]-(n-2)*a[n-2]; od; a; # _G. C. Greubel_, Oct 02 2019

%K sign

%O 0,4

%A _Zak Seidov_, Oct 17 2006

%E Terms a(21) onward added by _G. C. Greubel_, Oct 02 2019