A299967 Number of normal generalized Young tableaux of size n with all rows and columns weakly increasing and all regions non-singleton skew-partitions.

1, 0, 2, 3, 13, 32, 121, 376, 1406, 5030, 19632, 76334, 314582, 1308550, 5667494, 24940458, 113239394, 523149560, 2480434938, 11968944532, 59051754824

Offset: 0

Author

Gus Wiseman, Feb 22 2018

Keywords

• nonn
• more

Comments

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(4) = 13 tableaux:
1 1 2 2   1 1 1 1
.
1 2 2   1 1 2   1 1 1
1       2       1
.
1 2   1 1   1 1
1 2   2 2   1 1
.
1 2  1 1   1 1
1    2     1
2    2     1
.
1   1
1   1
2   1
2   1
		

Crossrefs

Cf. A000085, A063834, A138178, A153452, A238690, A296188, A297388, A299925, A299926, A299966.

Programs

Mathematica

undptns[y_]:=DeleteCases[Select[Tuples[Range[0,#]&/@y],OrderedQ[#,GreaterEqual]&],0,{2}];
ehn[y_]:=ehn[y]=If[Total[y]=!=1,1,0]+Sum[ehn[c],{c,Select[undptns[y],Total[#]>1&&Total[y]-Total[#]>1&]}];
Table[Sum[ehn[y],{y,IntegerPartitions[n]}],{n,15}]