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A323794
Number of non-isomorphic weight-n multisets of sets of multisets.
9
1, 1, 5, 17, 77, 318, 1561, 7667
OFFSET
0,3
COMMENTS
Also the number of non-isomorphic set multipartitions of multiset partitions of weight n.
All sets and multisets must be finite, and only the outermost may be empty.
The weight of an atom is 1, and the weight of a multiset is the sum of weights of its elements, counting multiplicity.
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(3) = 17 multiset partitions:
{{1}} {{11}} {{111}}
{{12}} {{112}}
{{1}{2}} {{123}}
{{1}}{{1}} {{1}{11}}
{{1}}{{2}} {{1}{12}}
{{1}{23}}
{{2}{11}}
{{1}}{{11}}
{{1}}{{12}}
{{1}}{{23}}
{{1}{2}{3}}
{{2}}{{11}}
{{1}}{{1}{2}}
{{1}}{{2}{3}}
{{1}}{{1}}{{1}}
{{1}}{{1}}{{2}}
{{1}}{{2}}{{3}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jan 28 2019
STATUS
approved