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A369192
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Number of labeled simple graphs with n vertices and at most n edges (not necessarily covering).
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13
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1, 1, 2, 8, 57, 638, 9949, 198440, 4791323, 135142796, 4346814276, 156713948672, 6251579884084, 273172369790743, 12969420360339724, 664551587744173992, 36543412829258260135, 2146170890448154922648, 134053014635659737513358, 8872652968135849629240560
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} binomial(binomial(n,2),k).
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EXAMPLE
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The a(0) = 1 through a(3) = 8 graphs:
{} {} {} {}
{{1,2}} {{1,2}}
{{1,3}}
{{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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Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Length[#]<=n&]], {n, 0, 5}]
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CROSSREFS
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Counting only covered vertices gives A369193.
A054548 counts graphs covering n vertices with k edges, with loops A369199.
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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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