A323789 Number of non-isomorphic weight-n sets of sets of multisets.

1, 1, 4, 15, 64, 269, 1310, 6460

Offset

0,3

Comments

Also the number of non-isomorphic strict multiset partitions, with strict parts, 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) = 15 multiset partition partitions:
  {{1}}  {{11}}      {{111}}
         {{12}}      {{112}}
         {{1}{2}}    {{123}}
         {{1}}{{2}}  {{1}{11}}
                     {{1}{12}}
                     {{1}{23}}
                     {{2}{11}}
                     {{1}}{{11}}
                     {{1}}{{12}}
                     {{1}}{{23}}
                     {{1}{2}{3}}
                     {{2}}{{11}}
                     {{1}}{{1}{2}}
                     {{1}}{{2}{3}}
                     {{1}}{{2}}{{3}}

Crossrefs

Cf. A007716, A049311, A050343, A283877, A316980, A317791, A318564, A318565, A318566, A318812.

Cf. A323787, A323788, A323790, A323791, A323792, A323793, A323794, A323795.

Sequence in context: A124541 A353264 A117669 * A341922 A007526 A233536

Adjacent sequences: A323786 A323787 A323788 * A323790 A323791 A323792

Keyword

nonn,more

Author

Gus Wiseman, Jan 27 2019

Status

approved