A323793 Number of non-isomorphic weight-n multisets of multisets of sets.

1, 1, 5, 15, 65, 240, 1090, 4845

Offset: 0

Author

Gus Wiseman, Jan 27 2019

Keywords

• nonn
• more

Comments

Also the number of non-isomorphic multiset partitions of set multipartitions 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) = 15 multiset partitions:
  {{1}}  {{12}}      {{123}}
         {{1}{1}}    {{1}{12}}
         {{1}{2}}    {{1}{23}}
         {{1}}{{1}}  {{1}{1}{1}}
         {{1}}{{2}}  {{1}}{{12}}
                     {{1}{1}{2}}
                     {{1}}{{23}}
                     {{1}{2}{3}}
                     {{1}}{{1}{1}}
                     {{1}}{{1}{2}}
                     {{1}}{{2}{3}}
                     {{2}}{{1}{1}}
                     {{1}}{{1}}{{1}}
                     {{1}}{{1}}{{2}}
                     {{1}}{{2}}{{3}}
		

Crossrefs

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

Cf. A323787, A323788, A323789, A323790, A323791, A323792, A323794, A323795.