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A299926
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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.
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16
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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
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1,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..20.
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EXAMPLE
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The a(3) = 14 tableaux:
1 2 3 1 2 2 1 1 2 1 1 1
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1 3 1 2 1 2 1 2 1 1 1 1
2 3 2 1 2 1
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1 1 1 1
2 2 1 1
3 2 2 1
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A000085, A063834, A138178, A153452, A296188, A296561, A297388, A299699, A299925.
Sequence in context: A241706 A111276 A149493 * A307399 A307411 A349018
Adjacent sequences: A299923 A299924 A299925 * A299927 A299928 A299929
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KEYWORD
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nonn,more
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AUTHOR
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Gus Wiseman, Feb 21 2018
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STATUS
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approved
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