A299926 - OEIS

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.

1, 4, 14, 60, 252, 1212, 5880, 30904, 166976, 952456, 5587840, 34217216, 215204960, 1401551376, 9360467760, 64384034784, 453328282624, 3274696185568, 24173219998912, 182546586425408

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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.

LINKS

Table of n, a(n) for n=1..20.

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}];