A129461 Fourth column (m=3) of triangle A129065.

1, 28, 908, 37896, 2036592, 138517632, 11692594944, 1202885199360, 148407122764800, 21652192199577600, 3690199478509977600, 726862474705593139200, 163918208008013340672000

Offset: 0

Author

Wolfdieter Lang, May 04 2007

Keywords

• nonn
• easy

Comments

See A129065 for the M. Bruschi et al. reference.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..245

Crossrefs

Cf. A129065, A129460 (m=2).

Programs

Magma

function T(n,k) // T = A129065
  if k lt 0 or k gt n then return 0;
  elif n eq 0 then return 1;
  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);
  end if;
end function;
A129461:= func< n | T(n+3, 3) >;
[A129461(n): n in [0..20]]; // G. C. Greubel, Feb 08 2024

Mathematica

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 *)
A129461[n_]:= T[n+3,3];
Table[A129461[n], {n,0,40}] (* G. C. Greubel, Feb 08 2024 *)

SageMath

@CachedFunction
def T(n,k): # T = A129065
    if (k<0 or k>n): return 0
    elif (n==0): return 1
    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)
def A129461(n): return T(n+3,3)
[A129461(n) for n in range(41)] # G. C. Greubel, Feb 08 2024

Formula

a(n) = A129065(n+3, 3), n >= 0.