login
A323795
Number of non-isomorphic weight-n sets of non-overlapping sets of sets.
17
1, 1, 3, 8, 27, 82, 310, 1163
OFFSET
0,3
COMMENTS
Also the number of non-isomorphic set partitions of set-systems 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(4) = 27 multiset partitions:
{{1}} {{12}} {{123}} {{1234}}
{{1}{2}} {{1}{12}} {{1}{123}}
{{1}}{{2}} {{1}{23}} {{12}{13}}
{{1}}{{12}} {{1}{234}}
{{1}}{{23}} {{12}{34}}
{{1}{2}{3}} {{1}}{{123}}
{{1}}{{2}{3}} {{1}{2}{12}}
{{1}}{{2}}{{3}} {{1}{2}{13}}
{{12}}{{13}}
{{1}}{{234}}
{{1}{2}{34}}
{{12}}{{34}}
{{1}}{{2}{12}}
{{12}}{{1}{2}}
{{1}}{{2}{13}}
{{12}}{{1}{3}}
{{1}}{{2}{34}}
{{1}{2}{3}{4}}
{{12}}{{3}{4}}
{{2}}{{1}{13}}
{{1}}{{2}}{{12}}
{{1}}{{2}}{{13}}
{{1}}{{2}}{{34}}
{{1}}{{2}{3}{4}}
{{1}{2}}{{3}{4}}
{{1}}{{2}}{{3}{4}}
{{1}}{{2}}{{3}}{{4}}
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jan 28 2019
STATUS
approved