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A299926
a(n) is the number of normal generalized Young tableaux of size n with all rows and columns weakly increasing and all regions skew partitions.
16
1, 4, 14, 60, 252, 1212, 5880, 30904, 166976, 952456, 5587840, 34217216, 215204960, 1401551376, 9360467760, 64384034784, 453328282624, 3274696185568, 24173219998912, 182546586425408
OFFSET
1,2
COMMENTS
If y is an integer partition of n, 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(3) = 14 tableaux:
1 2 3 1 2 2 1 1 2 1 1 1
.
1 3 1 2 1 2 1 2 1 1 1 1
2 3 2 1 2 1
.
1 1 1 1
2 2 1 1
3 2 2 1
MATHEMATICA
undptns[y_]:=DeleteCases[Select[Tuples[Range[0, #]&/@y], OrderedQ[#, GreaterEqual]&], 0, {2}];
chn[y_]:=Join[{{{}, y}}, Join@@Function[c, Append[#, y]&/@chn[c]]/@Take[undptns[y], {2, -2}]];
Table[Sum[Length[chn[y]], {y, IntegerPartitions[n]}], {n, 8}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Feb 21 2018
STATUS
approved