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

1,3

Links

Table of n, a(n) for n=1..14.

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

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

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 *)

Crossrefs

Sequence in context: A144347 A359453 A272959 * A061065 A210356 A328261

Adjacent sequences: A095348 A095349 A095350 * A095352 A095353 A095354

Keyword

nonn

Author

Eric W. Weisstein, Jun 03 2004

Extensions

More terms from Vladeta Jovovic, Jun 05 2004

Status

approved