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%I #19 Sep 04 2017 09:01:55
%S 0,1,12,192,5120,245760,22020096,3758096384,1236950581248,
%T 791648371998720,990791918021509120,2434970217729660813312,
%U 11787026741242634453385216,112652543574969605015820304384
%N Total number of edges in all labeled graphs on n nodes.
%H Maxie D. Schmidt, <a href="https://arxiv.org/abs/1609.02803">Square Series Generating Function Transformations</a>, arXiv preprint arXiv:1609.02803 [math.NT], 2016.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphEdge.html">Graph Edge</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LabeledGraph.html">Labeled Graph</a>
%F a(n) = (n*(n-1)/4)*2^(n*(n-1)/2). - _Vladeta Jovovic_, Jun 05 2004
%F a(n) = Sum_{k=0..binomial(n,2)} A084546(n,k)*k. - _Geoffrey Critzer_, Sep 04 2013
%t Table[(n*(n-1)/4)2^(n*(n-1)/2),{n,20}] (* _Harvey P. Dale_, Aug 16 2012 *)
%t nn=14;f[x_,y_]:=Sum[(1+y)^Binomial[n,2]x^n/n!,{n,0,nn}];Drop[Range[0,nn]!CoefficientList[Series[a=D[f[x,y],y]/.y->1,{x,0,nn}],x],1] (* _Geoffrey Critzer_, Sep 04 2013 *)
%K nonn
%O 1,3
%A _Eric W. Weisstein_, Jun 03 2004
%E More terms from _Vladeta Jovovic_, Jun 05 2004
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