A323794 Number of non-isomorphic weight-n multisets of sets of multisets.

1, 1, 5, 17, 77, 318, 1561, 7667

Offset: 0

Author

Gus Wiseman, Jan 28 2019

Keywords

• nonn
• more

Comments

Also the number of non-isomorphic set multipartitions 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.

Examples

			Non-isomorphic representatives of the a(1) = 1 through a(3) = 17 multiset partitions:
  {{1}}  {{11}}      {{111}}
         {{12}}      {{112}}
         {{1}{2}}    {{123}}
         {{1}}{{1}}  {{1}{11}}
         {{1}}{{2}}  {{1}{12}}
                     {{1}{23}}
                     {{2}{11}}
                     {{1}}{{11}}
                     {{1}}{{12}}
                     {{1}}{{23}}
                     {{1}{2}{3}}
                     {{2}}{{11}}
                     {{1}}{{1}{2}}
                     {{1}}{{2}{3}}
                     {{1}}{{1}}{{1}}
                     {{1}}{{1}}{{2}}
                     {{1}}{{2}}{{3}}
		

Crossrefs

Cf. A007716, A049311, A283877, A306186, A316980, A317791, A318565, A318566.

Cf. A323787, A323788, A323789, A323790, A323791, A323792, A323793, A323795.