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A299967
Number of normal generalized Young tableaux of size n with all rows and columns weakly increasing and all regions non-singleton skew-partitions.
2
1, 0, 2, 3, 13, 32, 121, 376, 1406, 5030, 19632, 76334, 314582, 1308550, 5667494, 24940458, 113239394, 523149560, 2480434938, 11968944532, 59051754824
OFFSET
0,3
COMMENTS
A generalized Young tableau of shape y is an array obtained by replacing the dots in the Ferrers diagram of y with positive integers. A tableau is normal if its entries span an initial interval of positive integers.
EXAMPLE
The a(4) = 13 tableaux:
1 1 2 2 1 1 1 1
.
1 2 2 1 1 2 1 1 1
1 2 1
.
1 2 1 1 1 1
1 2 2 2 1 1
.
1 2 1 1 1 1
1 2 1
2 2 1
.
1 1
1 1
2 1
2 1
MATHEMATICA
undptns[y_]:=DeleteCases[Select[Tuples[Range[0, #]&/@y], OrderedQ[#, GreaterEqual]&], 0, {2}];
ehn[y_]:=ehn[y]=If[Total[y]=!=1, 1, 0]+Sum[ehn[c], {c, Select[undptns[y], Total[#]>1&&Total[y]-Total[#]>1&]}];
Table[Sum[ehn[y], {y, IntegerPartitions[n]}], {n, 15}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Feb 22 2018
STATUS
approved