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A129460 Third column (m=2) of triangle A129065.

%I A129460 #13 Feb 08 2024 08:45:50
%S A129460 1,10,156,3696,125280,5780160,349090560,26760222720,2540101939200,
%T A129460 292579402752000,40213832085504000,6502800338141184000,
%U A129460 1222285449585328128000,264279998869470904320000
%N A129460 Third column (m=2) of triangle A129065.
%C A129460 See A129065 for the M. Bruschi et al. reference.
%H A129460 G. C. Greubel, <a href="/A129460/b129460.txt">Table of n, a(n) for n = 0..250</a>
%F A129460 a(n) = A129065(n+2, 2), n >= 0.
%t A129460 T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[n==0, 1, 2*(n-1)^2*T[n-1,k] - 4*Binomial[n-1,2]^2*T[n-2,k] +T[n-1,k-1] ]]; (* T=A129065 *)
%t A129460 A129460[n_]:= T[n+2,2];
%t A129460 Table[A129460[n], {n,0,40}] (* _G. C. Greubel_, Feb 08 2024 *)
%o A129460 (Magma)
%o A129460 function T(n,k) // T = A129065
%o A129460   if k lt 0 or k gt n then return 0;
%o A129460   elif n eq 0 then return 1;
%o A129460   else return 2*(n-1)^2*T(n-1,k) - 4*Binomial(n-1,2)^2*T(n-2,k) + T(n-1,k-1);
%o A129460   end if;
%o A129460 end function;
%o A129460 A129460:= func< n | T(n+2, 2) >;
%o A129460 [A129460(n): n in [0..20]]; // _G. C. Greubel_, Feb 08 2024
%o A129460 (SageMath)
%o A129460 @CachedFunction
%o A129460 def T(n,k): # T = A129065
%o A129460     if (k<0 or k>n): return 0
%o A129460     elif (n==0): return 1
%o A129460     else: return 2*(n-1)^2*T(n-1,k) - 4*binomial(n-1,2)^2*T(n-2,k) + T(n-1,k-1)
%o A129460 def A129460(n): return T(n+2,2)
%o A129460 [A129460(n) for n in range(41)] # _G. C. Greubel_, Feb 08 2024
%Y A129460 Cf. A129065, A129459 (m=1), A129461 (m=3).
%K A129460 nonn,easy
%O A129460 0,2
%A A129460 _Wolfdieter Lang_, May 04 2007