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A129466 Fourth column (m=3) sequence of triangle A129462 (v=2 member of a certain family).

%I A129466 #13 Feb 09 2024 02:01:23
%S A129466 1,12,208,5208,179688,8175744,472666752,33625704960,2858013642240,
%T A129466 281566521446400,30978996781363200,3583376917637529600,
%U A129466 374151199254884352000,9777217907401555968000,-16608590925355066982400000,-10323797933882945175552000000
%N A129466 Fourth column (m=3) sequence of triangle A129462 (v=2 member of a certain family).
%C A129466 See A129462 for the M. Bruschi et al. reference.
%H A129466 G. C. Greubel, <a href="/A129466/b129466.txt">Table of n, a(n) for n = 0..250</a>
%F A129466 a(n) = A129462(n+3,3), n >= 0.
%t A129466 T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[n==0, 1, (2*(n-1)*(n-2) - 1)*T[n-1,k] -((n-1)*(n-3))^2*T[n-2,k] +T[n-1,k-1]]];(*T=A129462*)
%t A129466 A129466[n_]:= T[n+3, 3];
%t A129466 Table[A129466[n], {n,0,40}] (* _G. C. Greubel_, Feb 09 2024 *)
%o A129466 (Magma)
%o A129466 function T(n, k) // T = A129462
%o A129466   if k lt 0 or k gt n then return 0;
%o A129466   elif n eq 0 then return 1;
%o A129466   else return (2*(n-1)*(n-2)-1)*T(n-1, k) - ((n-1)*(n-3))^2*T(n-2, k) + T(n-1, k-1);
%o A129466   end if;
%o A129466 end function;
%o A129466 A129466:= func< n | T(n+3,3) >;
%o A129466 [A129466(n): n in [0..20]]; // _G. C. Greubel_, Feb 09 2024
%o A129466 (SageMath)
%o A129466 @CachedFunction
%o A129466 def T(n, k): # T = A129462
%o A129466     if (k<0 or k>n): return 0
%o A129466     elif (n==0): return 1
%o A129466     else: return (2*(n-1)*(n-2)-1)*T(n-1, k) - ((n-1)*(n-3))^2*T(n-2, k) + T(n-1, k-1)
%o A129466 def A129466(n): return T(n+3,3)
%o A129466 [A129466(n) for n in range(41)] # _G. C. Greubel_, Feb 09 2024
%Y A129466 Cf. A129462, A129465 (m=2).
%K A129466 sign,easy
%O A129466 0,2
%A A129466 _Wolfdieter Lang_, May 04 2007