A321976 7-dimensional Catalan numbers.

1, 1, 429, 1385670, 13672405890, 278607172289160, 9490348077234178440, 475073684264389879228560, 32103104214166146088869942000, 2760171874087743799855959353857200, 289232890341906497299306268771988273600, 35764585916110766978895474668714467232388000

Offset: 0

Author

Seiichi Manyama, Nov 23 2018

Keywords

• nonn

Comments

Number of n X 7 Young tableaux.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..177
• Wikipedia, Hook length formula

Crossrefs

Row 7 of A060854.

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

Programs

GAP

List([0..15],n->24883200*Factorial(7*n)/Product([0..6],k->Factorial(n+k))); # Muniru A Asiru, Nov 25 2018

Magma

[24883200*Factorial(7*n) / (Factorial(n)*Factorial(n + 1)*Factorial(n + 2)*Factorial(n + 3)*Factorial(n + 4)*Factorial(n + 5)*Factorial(n + 6)): n in [0..15]]; // Vincenzo Librandi, Nov 24 2018

Mathematica

Table[24883200*(7*n)!/(n!*(n+1)!*(n+2)!*(n+3)!*(n+4)!*(n+5)!*(n+6)!),{n,0,15}] (* Vincenzo Librandi, Nov 24 2018 *)

PARI

{a(n) = 24883200*(7*n)!/(n!*(n+1)!*(n+2)!*(n+3)!*(n+4)!*(n+5)!*(n+6)!)}

Formula

a(n) = 0!*1!*...*6! * (7*n)! / ( n!*(n+1)!*...*(n+6)! ).

a(n) ~ 3110400 * 7^(7*n + 1/2) / (Pi^3 * n^24). - Vaclav Kotesovec, Nov 23 2018