A095351 Total number of edges in all labeled graphs on n nodes.

0, 1, 12, 192, 5120, 245760, 22020096, 3758096384, 1236950581248, 791648371998720, 990791918021509120, 2434970217729660813312, 11787026741242634453385216, 112652543574969605015820304384

Offset: 1

Author

Eric W. Weisstein, Jun 03 2004

Keywords

• nonn

Links

• Maxie D. Schmidt, Square Series Generating Function Transformations, arXiv preprint arXiv:1609.02803 [math.NT], 2016.
• Eric Weisstein's World of Mathematics, Graph Edge
• Eric Weisstein's World of Mathematics, Labeled Graph

Programs

Mathematica

Table[(n*(n-1)/4)2^(n*(n-1)/2),{n,20}] (* Harvey P. Dale, Aug 16 2012 *)
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 *)

Formula

a(n) = (n*(n-1)/4)*2^(n*(n-1)/2). - Vladeta Jovovic, Jun 05 2004

a(n) = Sum_{k=0..binomial(n,2)} A084546(n,k)*k. - Geoffrey Critzer, Sep 04 2013

Extensions

More terms from Vladeta Jovovic, Jun 05 2004