A321977 8-dimensional Catalan numbers.

1, 1, 1430, 23371634, 1489877926680, 231471904322784840, 67867669180627125604080, 32103104214166146088869942000, 22081374992701950398847674830857600, 20535535214275361308250745082811167425600, 24486819823897171791550434989846505231774984000

Offset: 0

Author

Seiichi Manyama, Nov 23 2018

Keywords

• nonn

Comments

Number of n X 8 Young tableaux.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..146
• Wikipedia, Hook length formula

Crossrefs

Row 8 of A060854.

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

Programs

GAP

List([0..15],n->125411328000*Factorial(8*n)/Product([0..7],k->Factorial(n+k))); # Muniru A Asiru, Nov 25 2018

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

Mathematica

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 *)

Formula

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

a(n) ~ 1913625 * 2^(24*n + 14) / (Pi^(7/2) * n^(63/2)). - Vaclav Kotesovec, Nov 23 2018