

A228129


a(n) = number of semistandard Young tableau families, headed by a father SSYT, containing daughter SSYT of shape equal to oncetrimmed father's shape, so that union of families equals all SSYT with sum of entries n.


1



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
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OFFSET

1,3


COMMENTS

Row sums of A228128.


LINKS

Table of n, a(n) for n=1..36.
N. Dragon, R. Stanley, SemiStandard Young Diagrams and families;


MATHEMATICA

(* hooklength: see A228125 *);
Tr/@Table[Tr[(SeriesCoefficient[q^(#1 . Range[Length[#1]])/Times @@ (1q^#1 &) /@ Flatten[hooklength[#1]], {q, 0, w}]& ) /@ Partitions[n]], {w, 24}, {n, w}]


CROSSREFS

Cf. A228128, A228125.
Sequence in context: A060482 A018138 A336631 * A175125 A171925 A186946
Adjacent sequences: A228126 A228127 A228128 * A228130 A228131 A228132


KEYWORD

nonn


AUTHOR

Wouter Meeussen, Aug 11 2013


STATUS

approved



