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A323790
Number of non-isomorphic weight-n sets of sets of sets.
11
1, 1, 3, 9, 33, 113, 474, 1985
OFFSET
0,3
COMMENTS
Non-isomorphic sets of sets are counted by A283877.
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) = 9 sets of sets of sets:
{{1}} {{12}} {{123}}
{{1}{2}} {{1}{12}}
{{1}}{{2}} {{1}{23}}
{{1}}{{12}}
{{1}}{{23}}
{{1}{2}{3}}
{{1}}{{1}{2}}
{{1}}{{2}{3}}
{{1}}{{2}}{{3}}
Non-isomorphic representatives of the a(4) = 33 sets of sets of sets:
{{1234}} {{1}{123}} {{1}{2}{12}} {{1}}{{1}{12}}
{{1}{234}} {{12}{13}} {{1}}{{2}{12}}
{{12}{34}} {{1}}{{123}} {{12}}{{1}{2}}
{{1}}{{234}} {{1}{2}{13}} {{1}}{{2}}{{12}}
{{1}{2}{34}} {{12}}{{13}} {{1}}{{2}}{{1}{2}}
{{12}}{{34}} {{1}}{{1}{23}}
{{1}}{{2}{34}} {{1}}{{2}{13}}
{{1}{2}{3}{4}} {{12}}{{1}{3}}
{{12}}{{3}{4}} {{2}}{{1}{13}}
{{1}}{{2}}{{34}} {{1}}{{1}{2}{3}}
{{1}}{{2}{3}{4}} {{1}}{{2}}{{13}}
{{1}{2}}{{3}{4}} {{1}{2}}{{1}{3}}
{{1}}{{2}}{{3}{4}} {{1}}{{2}}{{1}{3}}
{{1}}{{2}}{{3}}{{4}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jan 27 2019
STATUS
approved