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A248707 a(n) = f(3*n)/(f(n-1)*f(n)*f(n+1)), where f(k) = k!.

%I A248707 #24 Jun 11 2025 09:14:58
%S A248707 3,60,1260,27720,630630,14702688,349188840,8413788240,205086088350,
%T A248707 5046360719400,125149745841120,3124367780788800,78443948210518800,
%U A248707 1979201154850012800,50151543548788717200,1275619260617425959840,32554866547007225016750,833323952354971320243000
%N A248707 a(n) = f(3*n)/(f(n-1)*f(n)*f(n+1)), where f(k) = k!.
%C A248707 These are multinomial coefficients.
%H A248707 Clark Kimberling, <a href="/A248707/b248707.txt">Table of n, a(n) for n = 1..1000</a>
%F A248707 a(n) ~ 3^(3*n+1/2) / (2*Pi*n). - _Vaclav Kotesovec_, Oct 19 2014
%F A248707 From _Robert Israel_, Mar 02 2017: (Start)
%F A248707 G.f.: 3*x*hypergeom([4/3, 5/3], [3], 27*x).
%F A248707 n*(n+2)*a(n+1) = 3*(3*n+1)(3*n+2)*a(n). (End)
%e A248707 a(2) = 6!/(1!*2!*3!) = 60.
%p A248707 seq(3*(3*n-1)!/((n-1)!^3*n*(n+1)), n=1..20); # _Robert Israel_, Mar 02 2017
%t A248707 Table[(3 n)!/((n - 1)! n! (n + 1)!), {n, 1, 20}]
%o A248707 (Sage) [3*factorial(3*n-1)/(factorial(n-1)^3*n*(n+1)) for n in range(1,19)] # _Stefano Spezia_, Aug 16 2024
%o A248707 (PARI) a(n) = (3*n)! / ((n-1)!*n!*(n+1)!); \\ _Amiram Eldar_, Jun 11 2025
%Y A248707 Cf. A000142, A001700, A248708, A248709, A248710.
%K A248707 nonn,easy
%O A248707 1,1
%A A248707 _Clark Kimberling_, Oct 12 2014