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A369194
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Number of labeled loop-graphs covering n vertices with at most n edges.
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17
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1, 1, 4, 23, 199, 2313, 34015, 606407, 12712643, 306407645, 8346154699, 253476928293, 8490863621050, 310937199521774, 12356288017546937, 529516578044589407, 24339848939829286381, 1194495870124420574751, 62332449791125883072149, 3446265450868329833016605
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OFFSET
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0,3
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COMMENTS
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Row-sums of left portion of A369199.
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LINKS
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FORMULA
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Inverse binomial transform of A369196.
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EXAMPLE
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The a(0) = 1 through a(3) = 23 loop-graphs (loops shown as singletons):
{} {{1}} {{1,2}} {{1},{2,3}}
{{1},{2}} {{2},{1,3}}
{{1},{1,2}} {{3},{1,2}}
{{2},{1,2}} {{1,2},{1,3}}
{{1,2},{2,3}}
{{1},{2},{3}}
{{1,3},{2,3}}
{{1},{2},{1,3}}
{{1},{2},{2,3}}
{{1},{3},{1,2}}
{{1},{3},{2,3}}
{{2},{3},{1,2}}
{{2},{3},{1,3}}
{{1},{1,2},{1,3}}
{{1},{1,2},{2,3}}
{{1},{1,3},{2,3}}
{{2},{1,2},{1,3}}
{{2},{1,2},{2,3}}
{{2},{1,3},{2,3}}
{{3},{1,2},{1,3}}
{{3},{1,2},{2,3}}
{{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], {1, 2}]], Length[Union@@#]==n&&Length[#]<=n&]], {n, 0, 5}]
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CROSSREFS
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The version without loops is A369191.
A006125 counts simple graphs; also loop-graphs if shifted left.
A054548 counts graphs covering n vertices with k edges, with loops A369199.
Cf. A000169, A000272, A000666, A003465, A005703, A006649, A057500, A062740, A116508, A367862, A367916.
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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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