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A248710 a(n) = f(6*n+3)/(f(n-2)*f(n-1)*f(n)*f(n+1)*f(n+2)*f(n+3)), where f(k) = k!.

%I A248710 #14 Aug 16 2024 19:19:06
%S A248710 37837800,2053230379200,86825246363856000,3434459445168687936000,
%T A248710 133396980694935715950192000,5173935293233776678844146912000,
%U A248710 201687837026151453996918852912960000,7920886423528046052820994110450678080000,313629810506083768747620025974652020366480000
%N A248710 a(n) = f(6*n+3)/(f(n-2)*f(n-1)*f(n)*f(n+1)*f(n+2)*f(n+3)), where f(k) = k!.
%C A248710 These are multinomial coefficients.
%H A248710 Clark Kimberling, <a href="/A248710/b248710.txt">Table of n, a(n) for n = 2..200</a>
%F A248710 a(n) ~ 3^(5/2) * 6^(6*n+1) / (Pi^(5/2)*n^(5/2)). - _Vaclav Kotesovec_, Oct 19 2014
%e A248710 a(3) = 21!/(1!*2!*3!*4!*5!*6!) = 2053230379200.
%t A248710 Table[(6 n + 3)!/((n - 2)! (n - 1)! n! (n + 1)! (n + 2)! (n + 3)!), {n, 2, 20}]
%t A248710 Table[(6n+3)!/Times@@((n+Range[-2,3])!)  ,{n,2,20}] (* _Harvey P. Dale_, Jul 20 2020 *)
%o A248710 (Sage) [factorial(6*n + 3)/(factorial(n - 2)*factorial(n - 1)*factorial(n)*factorial(n + 1)*factorial(n + 2)*factorial(n + 3)) for n in range(2,11)] # _Stefano Spezia_, Aug 16 2024
%Y A248710 Cf. A000142, A001700, A248707, A248708, A248709.
%K A248710 nonn,easy
%O A248710 2,1
%A A248710 _Clark Kimberling_, Oct 12 2014