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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.

%I A245797 #19 Jan 11 2021 15:11:01
%S A245797 0,1,6,49,710,19011,954184,90154415,16108626420,5481798833245,
%T A245797 3582369649269620,4532127781040045649,11177949079089720090800,
%U A245797 54050029251399545975868271,514598463471970554205910304780,9677402372862708729859372687791391
%N A245797 The number of labeled graphs of n vertices that have endpoints, where an endpoint is a vertex with degree 1.
%H A245797 Andrew Howroyd, <a href="/A245797/b245797.txt">Table of n, a(n) for n = 1..50</a>
%F A245797 a(n) = 2^(n*(n+1)/2) - A059167(n).
%F A245797 Binomial transform of A327227 (assuming a(0) = 0).
%t A245797 m = 16;
%t A245797 egf = Exp[x^2/2]*Sum[2^Binomial[n, 2]*(x/Exp[x])^n/n!, {n, 0, m}];
%t A245797 A059167[n_] := SeriesCoefficient[egf, {x, 0, n}]*n!;
%t A245797 a[n_] := 2^(n(n-1)/2) - A059167[n];
%t A245797 Array[a, m] (* _Jean-François Alcover_, Feb 23 2019 *)
%t A245797 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],Min@@Length/@Split[Sort[Join@@#]]==1&]],{n,0,5}] (* _Gus Wiseman_, Sep 11 2019 *)
%Y A245797 Equal to row sums of A245796.
%Y A245797 The covering case is A327227.
%Y A245797 The connected case is A327362.
%Y A245797 The generalization to set-systems is A327228.
%Y A245797 BII-numbers of set-systems with minimum degree 1 are A327105.
%Y A245797 Cf. A001187, A006129, A059166, A059167, A100743, A136284, A327079, A327098, A327103, A327229, A327230.
%K A245797 nonn
%O A245797 1,3
%A A245797 _Chai Wah Wu_, Aug 01 2014
%E A245797 a(9)-a(16) from _Andrew Howroyd_, Oct 26 2017