OFFSET
0,2
COMMENTS
Number of standard Young tableaux of shape [5n,n].
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..260
Wikipedia, Young tableau
FORMULA
a(n) = C(6*n,n)*(4*n+1)/(5*n+1).
a(n) = [x^n] ((1 - sqrt(1 - 4*x))/(2*x))^(4*n+1). - Ilya Gutkovskiy, Nov 01 2017
Recurrence: 5*n*(4*n - 3)*(5*n - 3)*(5*n - 2)*(5*n - 1)*(5*n + 1)*a(n) = 72*(2*n - 1)*(3*n - 2)*(3*n - 1)*(4*n + 1)*(6*n - 5)*(6*n - 1)*a(n-1). - Vaclav Kotesovec, Feb 03 2018
MAPLE
a:= n-> binomial(6*n, n)*(4*n+1)/(5*n+1):
seq(a(n), n=0..20);
MATHEMATICA
Table[Binomial[6n, n] (4n+1)/(5n+1), {n, 0, 30}] (* Harvey P. Dale, Mar 06 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 15 2012
STATUS
approved