|
|
A323788
|
|
Number of non-isomorphic weight-n sets of multisets of multisets.
|
|
9
|
|
|
|
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
|
|
|
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.
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|