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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 (list; graph; refs; listen; history; text; internal format)
 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}]; 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}] CROSSREFS 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 KEYWORD nonn,more AUTHOR Gus Wiseman, Feb 21 2018 STATUS approved

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Last modified August 6 00:15 EDT 2024. Contains 374957 sequences. (Running on oeis4.)