

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 oncetrimmed 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
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OFFSET

1,13


COMMENTS

Row sums are A228129.
Reverse of rows seem to converge to first differences of A005986.


LINKS

Table of n, a(n) for n=1..120.
N. Dragon, R. Stanley, SemiStandard 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 @@ (1q^#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 A077042 A144903
Adjacent sequences: A228125 A228126 A228127 * A228129 A228130 A228131


KEYWORD

nonn,tabf


AUTHOR

Wouter Meeussen, Aug 11 2013


STATUS

approved



