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A323788 Number of non-isomorphic weight-n sets of multisets of multisets. 9
1, 1, 5, 19, 88, 391, 1995, 10281 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also the number of non-isomorphic strict multiset partitions 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) = 19 multiset partitions:

  {{1}}  {{11}}      {{111}}

         {{12}}      {{112}}

         {{1}{1}}    {{123}}

         {{1}{2}}    {{1}{11}}

         {{1}}{{2}}  {{1}{12}}

                     {{1}{23}}

                     {{2}{11}}

                     {{1}}{{11}}

                     {{1}{1}{1}}

                     {{1}}{{12}}

                     {{1}{1}{2}}

                     {{1}}{{23}}

                     {{1}{2}{3}}

                     {{2}}{{11}}

                     {{1}}{{1}{1}}

                     {{1}}{{1}{2}}

                     {{1}}{{2}{3}}

                     {{2}}{{1}{1}}

                     {{1}}{{2}}{{3}}

CROSSREFS

Cf. A005121, A007716, A049311, A050343, A283877, A306186, A316980, A317791, A318564, A318565, A318566, A318812.

Cf. A323787, A323789, A323790, A323791, A323792, A323793, A323794, A323795.

Sequence in context: A149799 A149800 A147099 * A154598 A184513 A149801

Adjacent sequences:  A323784 A323786 A323787 * A323789 A323790 A323791

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jan 27 2019

STATUS

approved

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Last modified October 14 16:48 EDT 2019. Contains 328022 sequences. (Running on oeis4.)