A327411 a(n) = multinomial(2*n+3; 3, 2, 2, ..., 2) (n times '2').

1, 10, 210, 7560, 415800, 32432400, 3405402000, 463134672000, 79196028912000, 16631166071520000, 4207685016094560000, 1262305504828368000000, 443069232194757168000000, 179886108271071410208000000, 83647040346048205746720000000, 44165637302713452634268160000000

Offset: 0

Author

Peter Luschny, Sep 07 2019

Keywords

• nonn

Crossrefs

Cf. A000457, A327412.

Programs

Maple

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

Mathematica

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

SageMath

def a(n):
    return multinomial([3] + [2] * n)
[a(n) for n in range(20)]

Formula

a(n) = 2^(-n-1)*Gamma(2*n + 4)/3.

a(n) = (2*(n-1)^2 + 9*n + 1)*a(n-1) for n > 0.

a(n) / n! = A000457(n).