A094594 Total number of edges in all connected labeled graphs on n nodes.

0, 1, 9, 144, 4140, 214200, 20264832, 3580049088, 1202974894656, 779257681804800, 982078160760512640, 2423077679970846226944, 11755368773275419420291072, 112487517660848696830655493120

Offset: 1

Author

Vladeta Jovovic, Jun 06 2004

Keywords

• easy
• nonn

Programs

Maple

a[1]:=0: for n from 1 to 16 do a[n]:= binomial(n,2)*2^(binomial(n,2)-1)-sum(binomial(n,k)*2^binomial(n-k,2)*a[k],k=1..n-1) od: seq(a[n],n=1..16); # Emeric Deutsch, Dec 18 2004

Mathematica

nn=14;f[x_,y_]:=Sum[(1+y)^Binomial[n,2]x^n/n!,{n,0,nn}];Drop[Range[0,nn]!CoefficientList[Series[D[Log[f[x,y]],y]/.y->1,{x,0,nn}],x],1] (* Geoffrey Critzer, Sep 04 2013 *)

Formula

E.g.f.: A(x)/B(x), where A(x) is e.g.f. of A095351 and B(x) is e.g.f. of A006125. recurrence: a(n) = binomial(n, 2)*2^(binomial(n, 2) - 1) - Sum_{k=1..n-1} binomial(n, k)*2^binomial(n-k, 2)*a(k).

a(n) = Sum_{k=0..binomial(n,2)} A062734(n,k)*k. - Geoffrey Critzer, Sep 04 2013

Extensions

More terms from Emeric Deutsch, Dec 18 2004