A323795 Number of non-isomorphic weight-n sets of non-overlapping sets of sets.

1, 1, 3, 8, 27, 82, 310, 1163

Offset: 0

Author

Gus Wiseman, Jan 28 2019

Keywords

• nonn
• more

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.

Examples

			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}}
		

Crossrefs

Cf. A004111, A007716, A049311, A050326, A050343, A283877, A306186, A318566.

Cf. A323787, A323788, A323789, A323790, A323791, A323792, A323793, A323794.