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A323786 Number of non-isomorphic weight-n multisets of multisets of non-singleton multisets. 0
1, 0, 2, 3, 19, 39, 200, 615 (list; graph; refs; listen; history; text; internal format)
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(4) = 19 multiset partitions:

  {{1111}}      {{1112}}      {{1123}}      {{1234}}

  {{11}{11}}    {{1122}}      {{11}{23}}    {{12}{34}}

  {{11}}{{11}}  {{11}{12}}    {{12}{13}}    {{12}}{{34}}

                {{11}{22}}    {{11}}{{23}}

                {{12}{12}}    {{12}}{{13}}

                {{11}}{{12}}

                {{11}}{{22}}

                {{12}}{{12}}

Non-isomorphic representatives of the a(5) = 39 multiset partitions:

  {{11111}}      {{11112}}      {{11123}}      {{11234}}      {{12345}}

  {{11}{111}}    {{11122}}      {{11223}}      {{11}{234}}    {{12}{345}}

  {{11}}{{111}}  {{11}{112}}    {{11}{123}}    {{12}{134}}    {{12}}{{345}}

                 {{11}{122}}    {{11}{223}}    {{23}{114}}

                 {{12}{111}}    {{12}{113}}    {{11}}{{234}}

                 {{12}{112}}    {{12}{123}}    {{12}}{{134}}

                 {{22}{111}}    {{13}{122}}    {{23}}{{114}}

                 {{11}}{{112}}  {{23}{111}}

                 {{11}}{{122}}  {{11}}{{123}}

                 {{12}}{{111}}  {{11}}{{223}}

                 {{12}}{{112}}  {{12}}{{113}}

                 {{22}}{{111}}  {{12}}{{123}}

                                {{13}}{{122}}

                                {{23}}{{111}}

CROSSREFS

Cf. A007716, A302545, A306186, A317791, A318564, A318566.

Cf. A323787, A323788, A323789, A323790, A323791, A323792, A323793, A323794.

Sequence in context: A135958 A265787 A163665 * A215381 A215377 A051079

Adjacent sequences:  A323782 A323783 A323784 * A323787 A323788 A323789

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jan 28 2019

STATUS

approved

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Last modified April 23 18:28 EDT 2019. Contains 322387 sequences. (Running on oeis4.)