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 A245797 The number of labeled graphs of n vertices that have endpoints, where an endpoint is a vertex with degree 1. 22
 0, 1, 6, 49, 710, 19011, 954184, 90154415, 16108626420, 5481798833245, 3582369649269620, 4532127781040045649, 11177949079089720090800, 54050029251399545975868271, 514598463471970554205910304780, 9677402372862708729859372687791391 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..50 FORMULA a(n) = 2^(n*(n+1)/2) - A059167(n). Binomial transform of A327227 (assuming a(0) = 0). MATHEMATICA m = 16; egf = Exp[x^2/2]*Sum[2^Binomial[n, 2]*(x/Exp[x])^n/n!, {n, 0, m}]; A059167[n_] := SeriesCoefficient[egf, {x, 0, n}]*n!; a[n_] := 2^(n(n-1)/2) - A059167[n]; Array[a, m] (* Jean-François Alcover, Feb 23 2019 *) Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Min@@Length/@Split[Sort[Join@@#]]==1&]], {n, 0, 5}] (* Gus Wiseman, Sep 11 2019 *) CROSSREFS Equal to row sums of A245796. The covering case is A327227. The connected case is A327362. The generalization to set-systems is A327228. BII-numbers of set-systems with minimum degree 1 are A327105. Cf. A001187, A006129, A059166, A059167, A100743, A136284, A327079, A327098, A327103, A327229, A327230. Sequence in context: A008786 A274278 A286799 * A046195 A305376 A024268 Adjacent sequences:  A245794 A245795 A245796 * A245798 A245799 A245800 KEYWORD nonn AUTHOR Chai Wah Wu, Aug 01 2014 EXTENSIONS a(9)-a(16) from Andrew Howroyd, Oct 26 2017 STATUS approved

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Last modified May 9 20:41 EDT 2021. Contains 343746 sequences. (Running on oeis4.)