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A369191
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Number of labeled simple graphs covering n vertices with at most n edges.
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15
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1, 0, 1, 4, 34, 387, 5686, 102084, 2162168, 52693975, 1450876804, 44509105965, 1504709144203, 55563209785167, 2224667253972242, 95984473918245388, 4439157388017620554, 219067678811211857307, 11489425098298623161164, 638159082104453330569185
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OFFSET
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0,4
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COMMENTS
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Row-sums of left portion of A054548.
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LINKS
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FORMULA
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Inverse binomial transform of A369193.
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EXAMPLE
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The a(0) = 1 through a(3) = 4 graphs:
{} . {{1,2}} {{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[Union@@#]==n&&Length[#]<=n&]], {n, 0, 5}]
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CROSSREFS
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This is the covering case of A369192, or A369193 for covered vertices.
The version for loop-graphs is A369194.
A054548 counts graphs covering n vertices with k edges, with loops A369199.
A057500 counts connected graphs with n vertices and n edges.
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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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