OFFSET
0,2
COMMENTS
Also the number of binary words with 6n 1's and 6 0's such that for every prefix the number of 1's is >= the number of 0's.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Wikipedia, Young tableau
FORMULA
G.f.: (5*x^6-35*x^5-609*x^4-11921*x^3-24892*x^2-9072*x-132)*x/(x-1)^7.
a(n) = (6*n-5)*(6*n+5)*(3*n+2)*(2*n+1)*(3*n+1)*(n+1)/10 for n>0, a(0) = 0.
MAPLE
a:= n-> max(0, (6*n-5)*(6*n+5)*(3*n+2)*(2*n+1)*(3*n+1)*(n+1)/10):
seq(a(n), n=0..40);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 16 2012
STATUS
approved