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A323793
Number of non-isomorphic weight-n multisets of multisets of sets.
9
1, 1, 5, 15, 65, 240, 1090, 4845
OFFSET
0,3
COMMENTS
Also the number of non-isomorphic multiset partitions of set multipartitions 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) = 15 multiset partitions:
{{1}} {{12}} {{123}}
{{1}{1}} {{1}{12}}
{{1}{2}} {{1}{23}}
{{1}}{{1}} {{1}{1}{1}}
{{1}}{{2}} {{1}}{{12}}
{{1}{1}{2}}
{{1}}{{23}}
{{1}{2}{3}}
{{1}}{{1}{1}}
{{1}}{{1}{2}}
{{1}}{{2}{3}}
{{2}}{{1}{1}}
{{1}}{{1}}{{1}}
{{1}}{{1}}{{2}}
{{1}}{{2}}{{3}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jan 27 2019
STATUS
approved