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A367863
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Number of n-vertex labeled simple graphs with n edges and no isolated vertices.
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52
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1, 0, 0, 1, 15, 222, 3760, 73755, 1657845, 42143500, 1197163134, 37613828070, 1295741321875, 48577055308320, 1969293264235635, 85852853154670693, 4005625283891276535, 199166987259400191480, 10513996906985414443720, 587316057411626070658200, 34612299496604684775762261
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(binomial(k,2), n). - Andrew Howroyd, Dec 29 2023
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EXAMPLE
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Non-isomorphic representatives of the a(4) = 15 graphs:
{{1,2},{1,3},{1,4},{2,3}}
{{1,2},{1,3},{2,4},{3,4}}
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MATHEMATICA
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Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#==Range[n]&&Length[#]==n&]], {n, 0, 5}]
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PROG
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(PARI) a(n) = sum(k=0, n, (-1)^(n-k) * binomial(n, k) * binomial(binomial(k, 2), n)) \\ Andrew Howroyd, Dec 29 2023
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CROSSREFS
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The non-covering version is A116508.
A143543 counts simple labeled graphs by number of connected components.
Cf. A003465, A006126, A305000, A316983, A319559, A323817, A326754, A367769, A367901, A367902, A367903.
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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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