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

Offset: 1

Author

Gus Wiseman, Feb 21 2018

Keywords

• nonn
• more

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.

Examples

			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
		

Crossrefs

Cf. A000085, A063834, A138178, A153452, A296188, A296561, A297388, A299699, A299925.

Programs

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}]