OFFSET
1,3
COMMENTS
Maximal element can be any integer, but is chosen here to be <=n.
LINKS
Alois P. Heinz, Rows n = 1..44, flattened
R. Stanley, Hook Lengths and Contents
EXAMPLE
For n=3 and k=2 the SSYT are
par= {3} SSYT= {{1, 1, 1}}, {{2, 1, 1}}, {{2, 2, 1}}, {{2, 2, 2}}
par= {2,1} SSYT= {{2, 1}, {1}}, {{2, 2}, {1}}
par= {1,1,1} SSYT= none
counts 4+2+0 = 6 = a(3,2).
Table begins:
1;
1, 4;
1, 6, 19;
1, 9, 39, 116;
1, 12, 69, 260, 751;
1, 16, 119, 560, 1955, 5552;
1, 20, 189, 1100, 4615, 15372, 43219; ...
MATHEMATICA
Needs["Combinatorica`"];
hooklength[(p_)?PartitionQ] := Block[{ferr = (PadLeft[1 + 0*Range[#1], Max[p]] &) /@ p}, DeleteCases[(Rest[FoldList[Plus, 0, #1]] &) /@ ferr + Reverse /@ Reverse[Transpose[(Rest[FoldList[Plus, 0, #1]] &) /@ Reverse[Reverse /@ Transpose[ferr]]]], 0, -1] - 1];
content[(p_)?PartitionQ]:= Block[{le= Max[p], ferr =(PadLeft[1+ 0*Range[#1], Max[p]]&) /@ p}, DeleteCases[ MapIndexed[-le+ Range[le, 1, -1]- #1- Tr[#2]&, 0*ferr]*ferr, 0, -1]+ le];
stanley[(p_)?PartitionQ, t_Integer] := Times @@ ((t + Flatten[content[p]])/Flatten[hooklength[p]]);
Table[Tr[ stanley[#, k] &/@ Partitions[n] ] , {n, 12}, {k, n}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Wouter Meeussen, Jun 12 2011
STATUS
approved