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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, 2849, 11174, 52377, 239269, 1191090, 6041975, 32275288, 177797719, 1017833092, 6014562272, 36717301665, 230947360981, 1495562098099, 9956230757240, 68070158777759, 477439197541792, 3432259679880648, 25267209686664449 (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
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}}
PROG
(PARI) \\ See links in A339645 for combinatorial species functions.
seq(n)={my(A=symGroupSeries(n)); NumUnlabeledObjsSeq(sCartProd(sExp(A), sExp(sExp(A-x*sv(1)))))} \\ Andrew Howroyd, Jan 17 2023
CROSSREFS
Sequence in context: A135958 A265787 A163665 * A215381 A215377 A051079
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 28 2019
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, Jan 17 2023
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)