A215547 Number of standard Young tableaux of shape [7n,7].

0, 429, 62016, 807300, 5101360, 21732542, 71916768, 199448964, 485325150, 1067658735, 2167714560, 4122884232, 7427426292, 12781794760, 21151379600, 33835482648, 52547352546, 79506102225, 117541332480, 170211285180, 241935349656, 338141745810, 465431207488

Offset: 0

Author

Alois P. Heinz, Aug 16 2012

Keywords

• nonn

Comments

Also the number of binary words with 7n 1's and 7 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=7 of A214776.

Programs

Maple

a:= n-> max(0, binomial(7*n+7,7)*(7*n-6)/(7*n+1)):
seq(a(n), n=0..30);

Mathematica

Join[{0},Table[Binomial[7n+7,7] (7n-6)/(7n+1),{n,30}]] (* Harvey P. Dale, Jul 24 2016 *)

Formula

G.f.: (6*x^7 -48*x^6 +2808*x^5 +83196*x^4 +355384*x^3 +323184*x^2 +58584*x +429)*x / (x-1)^8.

a(n) = C(7*n+7,7)*(7*n-6)/(7*n+1) for n>0, a(0) = 0.