A321975 6-dimensional Catalan numbers.
1, 1, 132, 87516, 140229804, 396499770810, 1671643033734960, 9490348077234178440, 67867669180627125604080, 583692803893929928888544400, 5838544419011620940996212276800, 66244124978105851196543024492572800, 836288764382254532915188713779640302400, 11570895443447601081407359451642915869302000
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..222
- Wikipedia, Hook length formula
Programs
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GAP
List([0..15],n->34560*Factorial(6*n)/Product([0..5],k->Factorial(n+k))); # Muniru A Asiru, Nov 25 2018
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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
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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
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Mathematica
Table[34560 (6 n)! / (n! (n + 1)! (n + 2)! (n + 3)! (n + 4)! (n + 5)!), {n, 0, 60}] (* Vincenzo Librandi, Nov 24 2018 *) -
PARI
{a(n) = 34560*(6*n)!/(n!*(n+1)!*(n+2)!*(n+3)!*(n+4)!*(n+5)!)}
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
Comments