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A299968
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Number of normal generalized Young tableaux of size n with all rows and columns strictly increasing.
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16
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1, 1, 2, 5, 15, 51, 189, 753, 3248, 14738, 70658, 354178, 1857703, 10121033, 57224955, 334321008, 2017234773, 12530668585, 80083779383, 525284893144, 3533663143981, 24336720018666, 171484380988738, 1234596183001927, 9075879776056533, 68052896425955296
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OFFSET
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0,3
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COMMENTS
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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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FORMULA
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EXAMPLE
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The a(4) = 15 tableaux:
1 2 3 4
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1 2 3 1 2 4 1 3 4 1 2 3 1 2 3
4 3 2 2 3
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1 2 1 3 1 2
3 4 2 4 2 3
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1 2 1 3 1 2 1 4 1 3
3 2 2 2 2
4 4 3 3 3
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1
2
3
4
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MATHEMATICA
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unddis[y_]:=DeleteCases[y-#, 0]&/@Tuples[Table[If[y[[i]]>Append[y, 0][[i+1]], {0, 1}, {0}], {i, Length[y]}]];
dos[y_]:=With[{sam=Rest[unddis[y]]}, If[Length[sam]===0, If[Total[y]===0, {{}}, {}], Join@@Table[Prepend[#, y]&/@dos[sam[[k]]], {k, 1, Length[sam]}]]];
Table[Sum[Length[dos[y]], {y, IntegerPartitions[n]}], {n, 1, 8}]
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CROSSREFS
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Cf. A000085, A000898, A001221, A005117, A006958, A015128, A138178, A238121, A238690, A285175, A296561, A297388, A299926, A300120, A300122.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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