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 A228128 T(n,m) = semistandard Young tableau families, headed by a father SSYT with shape a partition of k, 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. 2
 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 3, 3, 1, 1, 0, 1, 3, 4, 3, 1, 1, 0, 1, 4, 7, 5, 3, 1, 1, 0, 1, 5, 8, 9, 6, 3, 1, 1, 0, 1, 5, 13, 13, 10, 6, 3, 1, 1, 0, 1, 6, 14, 20, 17, 11, 6, 3, 1, 1, 0, 1, 7, 20, 27, 28, 19, 12, 6, 3, 1, 1, 0, 1, 7, 22, 38, 40, 33, 20, 12, 6, 3, 1, 1, 0, 1, 8, 29, 49, 60, 51, 37, 21, 12, 6, 3, 1, 1, 0, 1, 9, 31, 65, 85, 79, 59, 39, 22, 12, 6, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,13 COMMENTS Row sums are A228129. Reverse of rows seem to converge to first differences of A005986. LINKS N. Dragon, R. Stanley, Semi-Standard Young Diagrams and families; N. Dragon, résumé EXAMPLE T(6,3) = 3 since the 7 tableaux in the family contain 3 father tableaux: 11 , 13 , 1 4 2 2 3 see 2nd link, "content 6". MATHEMATICA (* hooklength: see A228125 *); 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. A228125, A228128, A228129. Sequence in context: A191607 A029387 A070878 * A060959 A342689 A077042 Adjacent sequences: A228125 A228126 A228127 * A228129 A228130 A228131 KEYWORD nonn,tabf AUTHOR Wouter Meeussen, Aug 11 2013 STATUS approved

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Last modified February 7 16:06 EST 2023. Contains 360128 sequences. (Running on oeis4.)