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

Author

Wouter Meeussen, Aug 11 2013

Keywords

• nonn

Comments

Row sums of A228128.

Links

• N. Dragon, R. Stanley, Semi-Standard Young Diagrams and families;

Crossrefs

Cf. A228128, A228125.

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}]