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A367869
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Number of labeled simple graphs covering n vertices and satisfying a strict version of the axiom of choice.
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42
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1, 0, 1, 4, 34, 387, 5596, 97149, 1959938, 44956945, 1154208544, 32772977715, 1019467710328, 34473686833527, 1259038828370402, 49388615245426933, 2070991708598960524, 92445181295983865757, 4376733266230674345874, 219058079619119072854095, 11556990682657196214302036
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OFFSET
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0,4
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COMMENTS
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The axiom of choice says that, given any set of nonempty sets Y, it is possible to choose a set containing an element from each. The strict version requires this set to have the same cardinality as Y, meaning no element is chosen more than once.
Number of labeled n-node graphs with at most one cycle in each component and no isolated vertices. - Andrew Howroyd, Dec 30 2023
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LINKS
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FORMULA
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EXAMPLE
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The a(3) = 4 graphs:
{{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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Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#==Range[n]&&Select[Tuples[#], UnsameQ@@#&]!={}&]], {n, 0, 5}]
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PROG
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(PARI) seq(n)={my(t=-lambertw(-x + O(x*x^n))); Vec(serlaplace(sqrt(1/(1-t))*exp(t/2 - 3*t^2/4 - x)))} \\ Andrew Howroyd, Dec 30 2023
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CROSSREFS
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A143543 counts simple labeled graphs by number of connected components.
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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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