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A321975 6-dimensional Catalan numbers.

%I A321975 #27 Sep 08 2022 08:46:23
%S A321975 1,1,132,87516,140229804,396499770810,1671643033734960,
%T A321975 9490348077234178440,67867669180627125604080,
%U A321975 583692803893929928888544400,5838544419011620940996212276800,66244124978105851196543024492572800,836288764382254532915188713779640302400,11570895443447601081407359451642915869302000
%N A321975 6-dimensional Catalan numbers.
%C A321975 Number of n X 6 Young tableaux.
%H A321975 Seiichi Manyama, <a href="/A321975/b321975.txt">Table of n, a(n) for n = 0..222</a>
%H A321975 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hook_length_formula">Hook length formula</a>
%F A321975 a(n) = 0!*1!*...*5! * (6*n)! / ( n!*(n+1)!*...*(n+5)! ).
%F A321975 a(n) ~ 5 * 2^(6*n + 6) * 3^(6*n + 7/2) / (Pi^(5/2) * n^(35/2)). - _Vaclav Kotesovec_, Nov 23 2018
%p A321975 a:= n-> (6*n)! * mul(i!/(6+i)!, i=0..n-1):
%p A321975 seq(a(n), n=0..14);  # _Alois P. Heinz_, Nov 25 2018
%t A321975 Table[34560 (6 n)! / (n! (n + 1)! (n + 2)! (n + 3)! (n + 4)! (n + 5)!), {n, 0, 60}] (* _Vincenzo Librandi_, Nov 24 2018 *)
%o A321975 (PARI) {a(n) = 34560*(6*n)!/(n!*(n+1)!*(n+2)!*(n+3)!*(n+4)!*(n+5)!)}
%o A321975 (Magma) [34560*Factorial(6*n)/(Factorial(n)*Factorial(n + 1)*Factorial(n + 2)*Factorial(n + 3)*Factorial(n + 4)*Factorial(n + 5)): n in [0..15]]; // _Vincenzo Librandi_, Nov 24 2018
%o A321975 (GAP) List([0..15],n->34560*Factorial(6*n)/Product([0..5],k->Factorial(n+k))); # _Muniru A Asiru_, Nov 25 2018
%Y A321975 Row 6 of A060854.
%Y A321975 Cf. A000108, A005789, A005790, A005791.
%K A321975 nonn
%O A321975 0,3
%A A321975 _Seiichi Manyama_, Nov 23 2018