A321975 6-dimensional Catalan numbers.

1, 1, 132, 87516, 140229804, 396499770810, 1671643033734960, 9490348077234178440, 67867669180627125604080, 583692803893929928888544400, 5838544419011620940996212276800, 66244124978105851196543024492572800, 836288764382254532915188713779640302400, 11570895443447601081407359451642915869302000

Offset

0,3

Comments

Number of n X 6 Young tableaux.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..222

Wikipedia, Hook length formula

Formula

a(n) = 0!*1!*...*5! * (6*n)! / ( n!*(n+1)!*...*(n+5)! ).

a(n) ~ 5 * 2^(6*n + 6) * 3^(6*n + 7/2) / (Pi^(5/2) * n^(35/2)). - Vaclav Kotesovec, Nov 23 2018

Maple

a:= n-> (6*n)! * mul(i!/(6+i)!, i=0..n-1):
seq(a(n), n=0..14);  # Alois P. Heinz, Nov 25 2018

Mathematica

Table[34560 (6 n)! / (n! (n + 1)! (n + 2)! (n + 3)! (n + 4)! (n + 5)!), {n, 0, 60}] (* Vincenzo Librandi, Nov 24 2018 *)

Prog

(PARI) {a(n) = 34560*(6*n)!/(n!*(n+1)!*(n+2)!*(n+3)!*(n+4)!*(n+5)!)}
(Magma) [34560*Factorial(6*n)/(Factorial(n)*Factorial(n + 1)*Factorial(n + 2)*Factorial(n + 3)*Factorial(n + 4)*Factorial(n + 5)): n in [0..15]]; // Vincenzo Librandi, Nov 24 2018
(GAP) List([0..15], n->34560*Factorial(6*n)/Product([0..5], k->Factorial(n+k))); # Muniru A Asiru, Nov 25 2018

Crossrefs

Row 6 of A060854.

Cf. A000108, A005789, A005790, A005791.

Sequence in context: A267951 A268098 A289294 * A289568 A368024 A114534

Adjacent sequences: A321972 A321973 A321974 * A321976 A321977 A321978

Keyword

nonn

Author

Seiichi Manyama, Nov 23 2018

Status

approved