A210428 Number of semistandard Young tableaux over all partitions of 6 with maximal element <= n.

0, 1, 16, 119, 560, 1955, 5552, 13573, 29632, 59229, 110320, 193963, 325040, 523055, 813008, 1226345, 1801984, 2587417, 3639888, 5027647, 6831280, 9145115, 12078704, 15758381, 20328896, 25955125, 32823856, 41145651, 51156784, 63121255, 77332880, 94117457

Offset: 0

Author

Alois P. Heinz, Mar 21 2012

Keywords

• nonn
• easy

Comments

a(n) is the number of semistandard Young tableaux over all partitions of 6 with maximal element <= n.

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Wikipedia, Young tableau
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Row n=6 of A210391.

Programs

Maple

a:= n-> n^2*(76+(85+19*n^2)*n^2)/180:
seq(a(n), n=0..40);

Formula

a(n) = n^2*(76+(85+19*n^2)*n^2)/180.

G.f.: -x*(x+1)*(x^4+8*x^3+20*x^2+8*x+1)/(x-1)^7.