%I #18 Aug 15 2017 03:09:01

%S 0,1,9,144,4140,214200,20264832,3580049088,1202974894656,

%T 779257681804800,982078160760512640,2423077679970846226944,

%U 11755368773275419420291072,112487517660848696830655493120

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

%F 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).

%F a(n) = Sum_{k=0..binomial(n,2)} A062734(n,k)*k. - _Geoffrey Critzer_, Sep 04 2013

%p 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

%t 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 *)

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Jun 06 2004

%E More terms from _Emeric Deutsch_, Dec 18 2004