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A129130
Number of triples of standard tableaux with the same shape of height less than or equal to three.
0
1, 1, 2, 10, 63, 531, 6201, 70477, 897149, 12772405, 188334604, 2939523104, 47902337803, 809518276503, 14134544880444, 252955559204532, 4651455689358657, 87356706437180529, 1669767921758484702
OFFSET
0,3
LINKS
F. Bergeron, L. Favreau and D. Krob, Conjectures on the enumeration of tableaux of bounded height, Discrete Math, vol. 139, no. 1-3 (1995), 463-468.
FORMULA
sum_lambda f_lambda^3 where the sum is over lambda partitions of length less than or equal to 3 and f_lambda is the number of standard tableaux of shape lambda
EXAMPLE
f_111 = f_3 = 1, f_21 = 2 therefore a(3) = f_111^3 + f_21^3 + f_3^3 = 1+8+1 = 10
CROSSREFS
KEYWORD
nonn
AUTHOR
Mike Zabrocki, Mar 30 2007
STATUS
approved