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

%I A327411 #19 Apr 19 2025 06:10:52
%S A327411 1,10,210,7560,415800,32432400,3405402000,463134672000,79196028912000,
%T A327411 16631166071520000,4207685016094560000,1262305504828368000000,
%U A327411 443069232194757168000000,179886108271071410208000000,83647040346048205746720000000,44165637302713452634268160000000
%N A327411 a(n) = multinomial(2*n+3; 3, 2, 2, ..., 2) (n times '2').
%F A327411 a(n) = 2^(-n-1)*Gamma(2*n + 4)/3.
%F A327411 a(n) = (2*(n-1)^2 + 9*n + 1)*a(n-1)  for n > 0.
%F A327411 a(n) / n! = A000457(n).
%p A327411 a:= n-> combinat[multinomial](2*n+3, 3, 2$n):
%p A327411 seq(a(n), n=0..17);  # _Alois P. Heinz_, Sep 07 2019
%t A327411 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A327411 a[n_] := multinomial[2n+3, Join[{3}, Table[2, {n}]]];
%t A327411 Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Apr 19 2025 *)
%o A327411 (SageMath)
%o A327411 def a(n):
%o A327411     return multinomial([3] + [2] * n)
%o A327411 [a(n) for n in range(20)]
%Y A327411 Cf. A000457, A327412.
%K A327411 nonn
%O A327411 0,2
%A A327411 _Peter Luschny_, Sep 07 2019