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%I #11 Sep 08 2022 08:45:27
%S 0,1,1,2,5,12,34,99,315,1042,3661,13354,51006,201561,826987,3498286,
%T 15277665,68578942,316519868,1497639547,7263576113,36035247374,
%U 182804409181,946808180148,5004540429504,26963932982089,148019711470333
%N a(n) = a(n-1) + (n-2)*a(n-2) + a(n-3) starting a(0)=0, a(1)=a(2)=1.
%H G. C. Greubel, <a href="/A121956/b121956.txt">Table of n, a(n) for n = 0..795</a>
%p with(combinat);
%p a:= proc(n) option remember;
%p if n<3 then fibonacci(n)
%p else a(n-1) + (n-2)*a(n-2) + a(n-3)
%p fi;
%p end:
%p seq(a(n), n=0..30); # _G. C. Greubel_, Oct 06 2019
%t M = {{0,1,0}, {0,0,1}, {1,n,1}}; v[0]= {0,1,1}; v[n_]:= v[n]= M.v[n-1]; Table[v[n][[1]], {n, 0, 30}]
%t a[n_]:= a[n]= If[n<3, Fibonacci[n], a[n-1] + (n-2)*a[n-2] + a[n-3]]; Table[a[n], {n,0,30}] (* _G. C. Greubel_, Oct 06 2019 *)
%o (PARI) my(m=30, v=concat([0,1,1], vector(m-3))); for(n=4, m, v[n]=v[n-1]+(n-3)*v[n-2]+v[n-3]); v \\ _G. C. Greubel_, Oct 06 2019
%o (Magma) I:=[0,1,1]; [n le 3 select I[n] else Self(n-1) + (n-3)*Self(n-2) + Self(n-3): n in [1..30]]; // _G. C. Greubel_, Oct 06 2019
%o (Sage)
%o @CachedFunction
%o def a(n):
%o if (n<3): return fibonacci(n)
%o else: return a(n-1) + (n-2)*a(n-2) + a(n-3)
%o [a(n) for n in (0..30)] # _G. C. Greubel_, Oct 06 2019
%o (GAP)
%o a:= function(n)
%o if n<3 then return Fibonacci(n);
%o else return a(n-1) + (n-2)*a(n-2) + a(n-3);
%o fi;
%o end;
%o List([0..30], n-> a(n) ); # _G. C. Greubel_, Oct 06 2019
%K nonn
%O 0,4
%A _Roger L. Bagula_, Sep 01 2006
%E Definition replaced by recurrence - the Assoc. Eds. of the OEIS, Mar 27 2010
%E Offset changed by _G. C. Greubel_, Oct 06 2019
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