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

1,3

Comments

Row sums of A228128.

Links

Table of n, a(n) for n=1..36.

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

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}]

Crossrefs

Cf. A228128, A228125.

Sequence in context: A060482 A018138 A336631 * A369695 A175125 A171925

Adjacent sequences: A228126 A228127 A228128 * A228130 A228131 A228132

Keyword

nonn

Author

Wouter Meeussen, Aug 11 2013

Status

approved