%I #16 Feb 29 2020 03:34:55

%S 1,10,560,92400,33633600,22870848000,26072766720000,46174869861120000,

%T 120054661638912000000,438679733628584448000000,

%U 2175851478797778862080000000,14240947928731462652313600000000,120136636726778618934917529600000000,1280656547507460077846220865536000000000

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

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

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

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

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

%p a:= n-> combinat[multinomial](3*n+2, 3$n, 2):

%p seq(a(n), n=0..17); # _Alois P. Heinz_, Sep 07 2019

%o (SageMath)

%o def a(n): return multinomial([2] + [3] * n)

%o [a(n) for n in range(15)]

%Y Cf. A014606, A327411, A025035.

%K nonn

%O 0,2

%A _Peter Luschny_, Sep 07 2019