A215548 Number of standard Young tableaux of shape [8n,8].

0, 1430, 389367, 7152444, 58261125, 303719922, 1188576675, 3804949176, 10495906641, 25810820750, 57928578191, 120681823860, 236332181085, 439263172458, 780774342075, 1335176857200, 2207407644585, 3542395893894, 5536432537895, 8450810096300, 12628017047349

Offset: 0

Author

Alois P. Heinz, Aug 16 2012

Keywords

• nonn

Comments

Also the number of binary words with 8n 1's and 8 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=8 of A214776.

Programs

Maple

a:= n-> max(0, binomial(8*n+8,8)*(8*n-7)/(8*n+1)):
seq(a(n), n=0..30);

Mathematica

Join[{0},Table[(Binomial[8n+8,8](8n-7))/(8n+1),{n,20}]] (* Harvey P. Dale, Mar 17 2020 *)

Formula

G.f.: (7*x^8 -63*x^7 -9615*x^6 -572643*x^5 -4331133*x^4 -7786221*x^3 -3699621*x^2 -376497*x -1430)*x / (x-1)^9.

a(n) = C(8*n+8,8)*(8*n-7)/(8*n+1) for n>0, a(0) = 0.