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

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

Offset

0,3

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.

Links

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

Example

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.

Sequence in context: A176645 A163133 A176574 * A241584 A176576 A110143

Adjacent sequences: A323789 A323790 A323791 * A323793 A323794 A323795

Keyword

nonn,more

Author

Gus Wiseman, Jan 27 2019

Status

approved