OFFSET
0,3
COMMENTS
Number of n X 9 Young tableaux.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..124
Wikipedia, Hook length formula
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
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 *)
PROG
(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
(GAP) List([0..10], n->5056584744960000*Factorial(9*n)/Product([0..8], k->Factorial(n+k))); # Muniru A Asiru, Nov 25 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 23 2018
STATUS
approved