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A305844
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Number of labeled spanning intersecting antichains on n vertices.
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39
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OFFSET
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0,4
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COMMENTS
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An intersecting antichain S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection, and none of which is a subset of any other. S is spanning if every vertex is contained in some edge.
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LINKS
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FORMULA
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Inverse binomial transform of A001206(n + 1).
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EXAMPLE
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The a(3) = 5 spanning intersecting antichains:
{{1,2,3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,3},{2,3}}
{{1,2},{1,3},{2,3}}
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MATHEMATICA
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Length/@Table[Select[Subsets[Rest[Subsets[Range[n]]]], And[Union@@#==Range[n], FreeQ[Intersection@@@Tuples[#, 2], {}, {1}], Select[Tuples[#, 2], UnsameQ@@#&&Complement@@#=={}&]=={}]&], {n, 1, 4}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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