A323791 Number of non-isomorphic weight-n sets of multisets of sets.

1, 1, 4, 13, 52, 196, 877, 3917

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) = 13 sets of multisets of sets:
  {{1}}  {{12}}      {{123}}
         {{1}{1}}    {{1}{12}}
         {{1}{2}}    {{1}{23}}
         {{1}}{{2}}  {{1}{1}{1}}
                     {{1}}{{12}}
                     {{1}{1}{2}}
                     {{1}}{{23}}
                     {{1}{2}{3}}
                     {{1}}{{1}{1}}
                     {{1}}{{1}{2}}
                     {{1}}{{2}{3}}
                     {{2}}{{1}{1}}
                     {{1}}{{2}}{{3}}

Crossrefs

Cf. A007716, A049311, A050326, A050343, A283877, A306186, A316980, A318564, A318565, A318566, A318812.

Cf. A323787, A323788, A323789, A323790, A323792, A323793, A323794, A323795.

Sequence in context: A357962 A097169 A149463 * A149464 A307398 A129147

Adjacent sequences: A323788 A323789 A323790 * A323792 A323793 A323794

Keyword

nonn,more

Author

Gus Wiseman, Jan 27 2019

Status

approved