A273396 Indecomposable collections of multisets with a total of n objects having entries {1,2,...,k} for some k<=n or INVERTi transform of A255906.

0, 1, 3, 9, 39, 201, 1227, 8305, 61383, 487761, 4131819, 37072361, 350644047, 3482957945, 36220558835, 393329507169, 4450157382383, 52354044069009, 639307054297779, 8090092395577625, 105935581968131399, 1433456549698679385, 20018656224312123051

Offset

0,3

Comments

A multiset partition of a multiset S is a set of nonempty multisets whose union is S. The total number of multisets of size n and whose entries have all the values in {1,2,...,k} for some k<=n is given by sequence A255906. A multiset partition is decomposable if there exists a value 1<=d<k such that every multiset A in the multiset partition either has max(A)<=d or min(A)>d. A multiset partition is called indecomposable otherwise.

References

P. A. MacMahon, Combinatory Analysis, vol 1, Cambridge, 1915.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

R. Orellana, M. Zabrocki, Symmetric group characters as symmetric functions, arXiv:1605.06672 [math.CO], 2016; or extended abstract, arXiv:1510.00438 [math.CO], 2015.

Example

a(3) = 9 because there are 16 multiset partitions, 9 of them are indecomposable ({{1},{1},{1}}, {{1},{1,1}}, {{1,1,1}}, {{1},{1,2}}, {{2},{1,2}}, {{1,1,2}}, {{1,2,2}}, {{2},{1,3}}, {{1,2,3}}) and 7 are decomposable ({{1},{1},{2}}, {{1},{2},{2}}, {{1},{2,2}}, {{2},{1,1}}, {{1},{2},{3}}, {{1},{2,3}}, {{3},{1,2}}).

Crossrefs

Cf. A074664, A003319.

INVERTi transform of A255906.

Sequence in context: A208816 A130905 A030799 * A058105 A090012 A340913

Adjacent sequences: A273393 A273394 A273395 * A273397 A273398 A273399

Keyword

nonn

Author

Mike Zabrocki, May 21 2016

Status

approved