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%I #8 Aug 13 2013 23:36:47
%S 1,1,2,3,5,9,13,22,34,53,80,125,184,279,413,610,891,1306,1883,2724,
%T 3902,5576,7919,11227,15808,22222,31085,43361,60242,83493,115261,
%U 158750,217925,298408,407430,554986
%N 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.
%C Row sums of A228128.
%H N. Dragon, R. Stanley, <a href="http://mathoverflow.net/questions/129854">Semi-Standard Young Diagrams and families</a>;
%t (* hooklength: see A228125 *);
%t 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}]
%Y Cf. A228128, A228125.
%K nonn
%O 1,3
%A _Wouter Meeussen_, Aug 11 2013
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