A215545 Number of standard Young tableaux of shape [5n,5].

0, 42, 1638, 10659, 40480, 115101, 272272, 566618, 1072764, 1888460, 3137706, 4973877, 7582848, 11186119, 16043940, 22458436, 30776732, 41394078, 54756974, 71366295, 91780416, 116618337, 146562808, 182363454, 224839900, 274884896, 333467442, 401635913

Offset: 0

Author

Alois P. Heinz, Aug 15 2012

Keywords

• nonn
• easy

Comments

Also the number of binary words with 5n 1's and 5 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
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Row n=5 of A214776.

Programs

Maple

a:= n-> max(0, (5*n-4)*(5*n+2)*(5*n+3)*(5*n+4)*(n+1)/24):
seq(a(n), n=0..40);

Formula

G.f.: (4*x^5-24*x^4+256*x^3+1461*x^2+1386*x+42)*x/(x-1)^6.

a(n) = (5*n-4)*(5*n+2)*(5*n+3)*(5*n+4)*(n+1)/24 for n>0, a(0) = 0.