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A368731
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Number of non-isomorphic n-element sets of nonempty subsets of {1..n}.
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5
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1, 1, 2, 10, 97, 2160, 126862, 21485262, 11105374322, 18109358131513, 95465831661532570, 1660400673336788987026, 96929369602251313489896310, 19268528295096123543660356281600, 13203875101002459910158494602665950757, 31517691852305548841992346407978317698725021
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OFFSET
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0,3
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LINKS
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EXAMPLE
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Non-isomorphic representatives of the a(3) = 10 set-systems:
{{1},{2},{3}}
{{1},{2},{1,2}}
{{1},{2},{1,3}}
{{1},{2},{1,2,3}}
{{1},{1,2},{1,3}}
{{1},{1,2},{2,3}}
{{1},{1,2},{1,2,3}}
{{1},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1,2},{1,3},{1,2,3}}
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MATHEMATICA
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brute[m_]:=First[Sort[Table[Sort[Sort /@ (m/.Rule@@@Table[{(Union@@m)[[i]], p[[i]]}, {i, Length[p]}])], {p, Permutations[Range[Length[Union@@m]]]}]]];
Table[Length[Union[brute /@ Subsets[Subsets[Range[n], {1, n}], {n}]]], {n, 0, 4}]
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PROG
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CROSSREFS
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The case of labeled covering graphs is A367863, binomial transform A367862.
These include the set-systems ranked by A367917.
Requiring all edges to be singletons or pairs gives A368598.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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