A323792 Number of non-isomorphic weight-n multisets of sets of sets.

1, 1, 4, 11, 43, 145, 614, 2549

Offset: 0

Author

Gus Wiseman, Jan 27 2019

Keywords

• nonn
• more

Comments

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) = 11 multiset partitions:
  {{1}}  {{12}}      {{123}}
         {{1}{2}}    {{1}{12}}
         {{1}}{{1}}  {{1}{23}}
         {{1}}{{2}}  {{1}}{{12}}
                     {{1}}{{23}}
                     {{1}{2}{3}}
                     {{1}}{{1}{2}}
                     {{1}}{{2}{3}}
                     {{1}}{{1}}{{1}}
                     {{1}}{{1}}{{2}}
                     {{1}}{{2}}{{3}}
		

Crossrefs

Cf. A007716, A049311, A050326, A050343, A255906, A283877, A306186, A316980, A318564, A318565, A318566.

Cf. A323787, A323788, A323789, A323790, A323791, A323793, A323794, A323795.