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

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

Offset

0,2

Comments

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

Links

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

Formula

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A129065, A129460 (m=2).

Sequence in context: A095656 A057412 A160263 * A239336 A203135 A097579

Adjacent sequences: A129458 A129459 A129460 * A129462 A129463 A129464

Keyword

nonn,easy

Author

Wolfdieter Lang, May 04 2007

Status

approved