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A210428
Number of semistandard Young tableaux over all partitions of 6 with maximal element <= n.
2
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
0,3
COMMENTS
a(n) is the number of semistandard Young tableaux over all partitions of 6 with maximal element <= n.
LINKS
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.
MAPLE
a:= n-> n^2*(76+(85+19*n^2)*n^2)/180:
seq(a(n), n=0..40);
CROSSREFS
Row n=6 of A210391.
Sequence in context: A200173 A226761 A250169 * A283037 A093740 A303724
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Mar 21 2012
STATUS
approved