A323787 Number of non-isomorphic multiset partitions of strict multiset partitions of weight n.

1, 1, 4, 14, 56, 219, 1001, 4588

Offset

0,3

Comments

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) = 14 multiset 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}}{{2}{3}}
                     {{1}}{{2}}{{3}}

Crossrefs

Cf. A002846, A005121, A007716, A050343, A213427, A269134, A283877, A306186, A316980, A317791, A318564, A318565, A318566, A318812.

Cf. A323788, A323789, A323790, A323791, A323792, A323793, A323794, A323795.

Sequence in context: A304977 A143406 A329777 * A132837 A259808 A149491

Adjacent sequences: A323784 A323785 A323786 * A323788 A323789 A323790

Keyword

nonn,more

Author

Gus Wiseman, Jan 27 2019

Status

approved