OFFSET
0,2
COMMENTS
Also the number of binary words with 9n 1's and 9 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.: (8*x^9 -80*x^8 +37540*x^7 +3833365*x^6 +48377194*x^5 +151114390*x^4 +142200850*x^3 +39434230*x^2 +2418130*x +4862)*x / (x-1)^10.
a(n) = C(9*n+9,9)*(9*n-8)/(9*n+1) for n>0, a(0) = 0.
MAPLE
a:= n-> max(0, binomial(9*n+9, 9)*(9*n-8)/(9*n+1)):
seq(a(n), n=0..30);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 16 2012
STATUS
approved