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

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

Offset

0,3

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.

Links

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

Example

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.

Sequence in context: A066886 A149617 A149618 * A149619 A149620 A149621

Adjacent sequences: A323790 A323791 A323792 * A323794 A323795 A323796

Keyword

nonn,more

Author

Gus Wiseman, Jan 27 2019

Status

approved