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%I A321977 #22 Sep 08 2022 08:46:23
%S A321977 1,1,1430,23371634,1489877926680,231471904322784840,
%T A321977 67867669180627125604080,32103104214166146088869942000,
%U A321977 22081374992701950398847674830857600,20535535214275361308250745082811167425600,24486819823897171791550434989846505231774984000
%N A321977 8-dimensional Catalan numbers.
%C A321977 Number of n X 8 Young tableaux.
%H A321977 Seiichi Manyama, <a href="/A321977/b321977.txt">Table of n, a(n) for n = 0..146</a>
%H A321977 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hook_length_formula">Hook length formula</a>
%F A321977 a(n) = 0!*1!*...*7! * (8*n)! / ( n!*(n+1)!*...*(n+7)! ).
%F A321977 a(n) ~ 1913625 * 2^(24*n + 14) / (Pi^(7/2) * n^(63/2)). - _Vaclav Kotesovec_, Nov 23 2018
%t A321977 Table[125411328000 (8 n)! / (n! (n+1)! (n+2)! (n+3)! (n+4)! (n+5)! (n+6)! (n + 7)!), {n, 0, 15}] (* _Vincenzo Librandi_, Nov 24 2018 *)
%o A321977 (Magma) [125411328000*Factorial(8*n)/(Factorial(n)*Factorial(n + 1)*Factorial(n + 2)*Factorial(n + 3)*Factorial(n + 4)*Factorial(n + 5)*Factorial(n + 6)*Factorial(n + 7)): n in [0..15]]; // _Vincenzo Librandi_, Nov 24 2018
%o A321977 (GAP) List([0..15],n->125411328000*Factorial(8*n)/Product([0..7],k->Factorial(n+k))); # _Muniru A Asiru_, Nov 25 2018
%Y A321977 Row 8 of A060854.
%Y A321977 Cf. A000108, A005789, A005790, A005791, A321975, A321976.
%K A321977 nonn
%O A321977 0,3
%A A321977 _Seiichi Manyama_, Nov 23 2018

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