A215549 - OEIS

%I #9 Feb 08 2017 18:35:36

%S 0,4862,2466750,63882940,670609940,4277470470,19794795118,73143988775,

%T 228723580800,628737007195,1559830082888,3559370252529,7576971259000,

%U 15210525840125,29040055455840,53087119860346,93432350566520,159028880903100,262755041438890

%N Number of standard Young tableaux of shape [9n,9].

%C 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.

%H Alois P. Heinz, <a href="/A215549/b215549.txt">Table of n, a(n) for n = 0..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>

%F 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.

%F a(n) = C(9*n+9,9)*(9*n-8)/(9*n+1) for n>0, a(0) = 0.

%p a:= n-> max(0, binomial(9*n+9,9)*(9*n-8)/(9*n+1)):

%p seq(a(n), n=0..30);

%Y Row n=9 of A214776.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Aug 16 2012