%I #22 Sep 08 2022 08:46:23

%S 1,1,1430,23371634,1489877926680,231471904322784840,

%T 67867669180627125604080,32103104214166146088869942000,

%U 22081374992701950398847674830857600,20535535214275361308250745082811167425600,24486819823897171791550434989846505231774984000

%N 8-dimensional Catalan numbers.

%C Number of n X 8 Young tableaux.

%H Seiichi Manyama, <a href="/A321977/b321977.txt">Table of n, a(n) for n = 0..146</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hook_length_formula">Hook length formula</a>

%F a(n) = 0!*1!*...*7! * (8*n)! / ( n!*(n+1)!*...*(n+7)! ).

%F a(n) ~ 1913625 * 2^(24*n + 14) / (Pi^(7/2) * n^(63/2)). - _Vaclav Kotesovec_, Nov 23 2018

%t 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 (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 (GAP) List([0..15],n->125411328000*Factorial(8*n)/Product([0..7],k->Factorial(n+k))); # _Muniru A Asiru_, Nov 25 2018

%Y Row 8 of A060854.

%Y Cf. A000108, A005789, A005790, A005791, A321975, A321976.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 23 2018