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

1, 12, 208, 5208, 179688, 8175744, 472666752, 33625704960, 2858013642240, 281566521446400, 30978996781363200, 3583376917637529600, 374151199254884352000, 9777217907401555968000, -16608590925355066982400000, -10323797933882945175552000000

Offset: 0

Author

Wolfdieter Lang, May 04 2007

Keywords

• sign
• easy

Comments

See A129462 for the M. Bruschi et al. reference.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A129462, A129465 (m=2).

Programs

Magma

function T(n, k) // T = A129462
  if k lt 0 or k gt n then return 0;
  elif n eq 0 then return 1;
  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);
  end if;
end function;
A129466:= func< n | T(n+3,3) >;
[A129466(n): n in [0..20]]; // G. C. Greubel, Feb 09 2024

Mathematica

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*)
A129466[n_]:= T[n+3, 3];
Table[A129466[n], {n,0,40}] (* G. C. Greubel, Feb 09 2024 *)

SageMath

@CachedFunction
def T(n, k): # T = A129462
    if (k<0 or k>n): return 0
    elif (n==0): return 1
    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)
def A129466(n): return T(n+3,3)
[A129466(n) for n in range(41)] # G. C. Greubel, Feb 09 2024

Formula

a(n) = A129462(n+3,3), n >= 0.