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

0,2

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

Row n=9 of A214776.

Sequence in context: A264182 A258496 A258397 * A295442 A227599 A321978

Adjacent sequences: A215546 A215547 A215548 * A215550 A215551 A215552

Keyword

nonn

Author

Alois P. Heinz, Aug 16 2012

Status

approved