A228129 a(n) = number of semistandard Young tableau families, headed by a father SSYT, containing daughter SSYT of shape equal to once-trimmed father's shape, so that union of families equals all SSYT with sum of entries n.
1, 1, 2, 3, 5, 9, 13, 22, 34, 53, 80, 125, 184, 279, 413, 610, 891, 1306, 1883, 2724, 3902, 5576, 7919, 11227, 15808, 22222, 31085, 43361, 60242, 83493, 115261, 158750, 217925, 298408, 407430, 554986
Offset: 1
Keywords
Links
- N. Dragon, R. Stanley, Semi-Standard Young Diagrams and families;
Programs
-
Mathematica
(* hooklength: see A228125 *); Tr/@Table[Tr[(SeriesCoefficient[q^(#1 . Range[Length[#1]])/Times @@ (1-q^#1 &) /@ Flatten[hooklength[#1]], {q, 0, w}]& ) /@ Partitions[n]], {w, 24}, {n, w}]
Comments