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

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

Offset

0,3

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.

Links

Table of n, a(n) for n=0..7.

Example

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.

Sequence in context: A149741 A149742 A149743 * A151479 A330800 A293458

Adjacent sequences: A323791 A323792 A323793 * A323795 A323796 A323797

Keyword

nonn,more

Author

Gus Wiseman, Jan 28 2019

Status

approved