A215549 Number of standard Young tableaux of shape [9n,9].

0, 4862, 2466750, 63882940, 670609940, 4277470470, 19794795118, 73143988775, 228723580800, 628737007195, 1559830082888, 3559370252529, 7576971259000, 15210525840125, 29040055455840, 53087119860346, 93432350566520, 159028880903100, 262755041438890

Offset: 0

Author

Alois P. Heinz, Aug 16 2012

Keywords

• nonn

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

Crossrefs

Row n=9 of A214776.

Programs

Maple

a:= n-> max(0, binomial(9*n+9,9)*(9*n-8)/(9*n+1)):
seq(a(n), n=0..30);

Formula

G.f.: (8*x^9 -80*x^8 +37540*x^7 +3833365*x^6 [phone]*x^5 [phone]*x^4 [phone]*x^3 [phone]*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.