OFFSET
0,3
COMMENTS
Also the number of binary words with n^2 1's and n 0's such that for every prefix the number of 1's is >= the number of 0's. The a(2) = 9 words are: 101011, 101101, 101110, 110011, 110101, 110110, 111001, 111010, 111100.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..337
Wikipedia, Young tableau
FORMULA
a(n) = C((n+1)*n, n)*((n-1)*n+1)/(n*n+1).
a(n) = A214776(n,n).
a(n) = [x^n] ((1 - sqrt(1 - 4*x))/(2*x))^(n^2-n+1). - Ilya Gutkovskiy, Nov 01 2017
MAPLE
a:= n-> binomial((n+1)*n, n)*((n-1)*n+1)/(n*n+1):
seq(a(n), n=0..20);
MATHEMATICA
Table[Binomial[n(n+1), n] (n(n-1)+1)/(n^2+1), {n, 0, 20}] (* Harvey P. Dale, Dec 08 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 16 2012
STATUS
approved