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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 September 25 21:49 EDT 2022. Contains 356986 sequences. (Running on oeis4.)