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 A327362 Number of labeled connected graphs covering n vertices with at least one endpoint (vertex of degree 1). 6
 0, 0, 1, 3, 28, 475, 14646, 813813, 82060392, 15251272983, 5312295240010, 3519126783483377, 4487168285715524124, 11116496280631563128723, 53887232400918561791887118, 513757147287101157620965656285, 9668878162669182924093580075565776 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A graph is covering if the vertex set is the union of the edge set, so there are no isolated vertices. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..50 FORMULA Inverse binomial transform of A327364. a(n) = A001187(n) - A059166(n). - Andrew Howroyd, Sep 11 2019 MATHEMATICA csm[s_]:=With[{c=Select[Subsets[Range[Length[s]], {2}], Length[Intersection@@s[[#]]]>0&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[]], Union@@s[[c[]]]]]]]]; Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#==Range[n]&&Length[csm[#]]==1&&Min@@Length/@Split[Sort[Join@@#]]==1&]], {n, 0, 5}] PROG (PARI) seq(n)={Vec(serlaplace(-x^2/2 + log(sum(k=0, n, 2^binomial(k, 2)*x^k/k! + O(x*x^n))) - log(sum(k=0, n, 2^binomial(k, 2)*(x*exp(-x + O(x^n)))^k/k!))), -(n+1))} \\ Andrew Howroyd, Sep 11 2019 CROSSREFS The non-connected version is A327227. The non-covering version is A327364. Graphs with endpoints are A245797. Connected covering graphs are A001187. Connected graphs with bridges are A327071. Cf. A004110, A059166, A006125, A006129, A059166, A100743, A141580, A322395, A327105, A327229, A327230, A327366, A327369, A327377. Sequence in context: A210854 A108288 A060545 * A327071 A058804 A327114 Adjacent sequences:  A327359 A327360 A327361 * A327363 A327364 A327365 KEYWORD nonn AUTHOR Gus Wiseman, Sep 04 2019 EXTENSIONS Terms a(7) and beyond from Andrew Howroyd, Sep 11 2019 STATUS approved

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Last modified April 11 16:42 EDT 2021. Contains 342888 sequences. (Running on oeis4.)