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

1, 10, 156, 3696, 125280, 5780160, 349090560, 26760222720, 2540101939200, 292579402752000, 40213832085504000, 6502800338141184000, 1222285449585328128000, 264279998869470904320000

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..250

Formula

a(n) = A129065(n+2, 2), 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 *)
A129460[n_]:= T[n+2, 2];
Table[A129460[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;
A129460:= func< n | T(n+2, 2) >;
[A129460(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 A129460(n): return T(n+2, 2)
[A129460(n) for n in range(41)] # G. C. Greubel, Feb 08 2024

Crossrefs

Cf. A129065, A129459 (m=1), A129461 (m=3).

Sequence in context: A246239 A235340 A306034 * A200989 A268883 A283721

Adjacent sequences: A129457 A129458 A129459 * A129461 A129462 A129463

Keyword

nonn,easy

Author

Wolfdieter Lang, May 04 2007

Status

approved