A321978 9-dimensional Catalan numbers.

1, 1, 4862, 414315330, 177295473274920, 219738059326729823880, 583692803893929928888544400, 2760171874087743799855959353857200, 20535535214275361308250745082811167425600, 220381378415074546123953914908618547085974856000

Offset: 0

Author

Seiichi Manyama, Nov 23 2018

Keywords

• nonn

Comments

Number of n X 9 Young tableaux.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..124
• Wikipedia, Hook length formula

Crossrefs

Row 9 of A060854.

Cf. A000108, A005789, A005790, A005791, A321975, A321976, A321977.

Programs

GAP

List([0..10],n->5056584744960000*Factorial(9*n)/Product([0..8],k->Factorial(n+k))); # Muniru A Asiru, Nov 25 2018

Magma

[5056584744960000*Factorial(9*n)/(Factorial(n)*Factorial(n + 1)*Factorial(n + 2)*Factorial(n + 3)*Factorial(n + 4)*Factorial(n + 5)*Factorial(n + 6)*Factorial(n + 7)*Factorial(n + 8)): n in [0..15]]; // Vincenzo Librandi, Nov 24 2018

Mathematica

Table[5056584744960000 (9 n)! / (n! (n + 1)! (n + 2)! (n + 3)! (n + 4)! (n + 5)! (n + 6)! (n + 7)! (n + 8)!), {n, 0, 15}] (* Vincenzo Librandi, Nov 24 2018 *)

Formula

a(n) = 0!*1!*...*8! * (9*n)! / ( n!*(n+1)!*...*(n+8)! ).

a(n) ~ 16056320000 * 3^(18*n + 10) / (Pi^4 * n^40). - Vaclav Kotesovec, Nov 23 2018