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A327078
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Binomial transform of A001187 (labeled connected graphs), if we assume A001187(1) = 0.
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2
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1, 1, 2, 8, 61, 969, 31738, 2069964, 267270033, 68629753641, 35171000942698, 36024807353574280, 73784587576805254653, 302228602363365451957793, 2475873310144021668263093202, 40564787336902311168400640561084
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OFFSET
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0,3
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COMMENTS
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Here we consider that there is no nonempty connected graph with one vertex (different from A001187 and A182100).
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LINKS
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FORMULA
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EXAMPLE
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The a(0) = 1 through a(3) = 8 edge-sets:
{} {} {} {}
{{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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MAPLE
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b:= proc(n) option remember; `if`(n=0, 1, 2^(n*(n-1)/2)-add(
k*binomial(n, k)*2^((n-k)*(n-k-1)/2)*b(k), k=1..n-1)/n)
end:
a:= n-> add(b(n-j)*binomial(n, j), j=0..n-2)+1:
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MATHEMATICA
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csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Length[csm[#]]<=1&]], {n, 0, 5}]
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CROSSREFS
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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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