A327412 a(n) = multinomial(3*n+2; 2, 3, 3, ..., 3) (n times '3').

1, 10, 560, 92400, 33633600, 22870848000, 26072766720000, 46174869861120000, 120054661638912000000, 438679733628584448000000, 2175851478797778862080000000, 14240947928731462652313600000000, 120136636726778618934917529600000000, 1280656547507460077846220865536000000000

Offset: 0

Author

Peter Luschny, Sep 07 2019

Keywords

• nonn

Crossrefs

Cf. A014606, A327411, A025035.

Programs

Maple

a:= n-> combinat[multinomial](3*n+2, 3$n, 2):
seq(a(n), n=0..17);  # Alois P. Heinz, Sep 07 2019

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
a[n_] := multinomial[3n+2, Join[{2}, Table[3, {n}]]];
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Apr 19 2025 *)

SageMath

def a(n): return multinomial([2] + [3] * n)
[a(n) for n in range(15)]

Formula

a(n) = 2^(-n-1)*3^(-n)*Gamma(3*n + 3).

a(n) = (9*(n-1)^3 + 36*(n-1)^2 + 47*n - 27)*a(n-1)/2 for n > 0.

a(n) / n! = A025035(n+1).

a(n)*(n+1) = A014606(n+1).