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A323789
Number of non-isomorphic weight-n sets of sets of multisets.
9
1, 1, 4, 15, 64, 269, 1310, 6460
OFFSET
0,3
COMMENTS
Also the number of non-isomorphic strict multiset partitions, with strict parts, 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) = 15 multiset partition partitions:
{{1}} {{11}} {{111}}
{{12}} {{112}}
{{1}{2}} {{123}}
{{1}}{{2}} {{1}{11}}
{{1}{12}}
{{1}{23}}
{{2}{11}}
{{1}}{{11}}
{{1}}{{12}}
{{1}}{{23}}
{{1}{2}{3}}
{{2}}{{11}}
{{1}}{{1}{2}}
{{1}}{{2}{3}}
{{1}}{{2}}{{3}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jan 27 2019
STATUS
approved