A215546 - OEIS

%I #9 Feb 08 2017 18:37:51

%S 0,132,9996,92092,451269,1570800,4395118,10559208,22664655,44602348,

%T 81921840,142247364,235740505,375609528,578665362,865924240,

%U 1263256995,1802085012,2520122836,3462167436,4680934125,6237939136,8204428854,10662355704,13705400695

%N Number of standard Young tableaux of shape [6n,6].

%C 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.

%H Alois P. Heinz, <a href="/A215546/b215546.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.: (5*x^6-35*x^5-609*x^4-11921*x^3-24892*x^2-9072*x-132)*x/(x-1)^7.

%F 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.

%p a:= n-> max(0, (6*n-5)*(6*n+5)*(3*n+2)*(2*n+1)*(3*n+1)*(n+1)/10):

%p seq(a(n), n=0..40);

%Y Row n=6 of A214776.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Aug 16 2012