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Total number of nodes in all simple graphs of n nodes.
2

%I #19 Aug 15 2019 14:20:15

%S 1,4,12,44,170,936,7308,98768,2472012,120051680,11208976504,

%T 1981094071104,656526407783376,406758179201296832,

%U 471397289547064631520,1024016251272440926318848,4180909690610059855623236192,32176399052621010609861807435264

%N Total number of nodes in all simple graphs of n nodes.

%H Alois P. Heinz, <a href="/A055542/b055542.txt">Table of n, a(n) for n = 1..87</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphVertex.html">Graph Vertex</a>

%p b:= proc(n, i, l) `if`(n=0 or i=1, 1/n!*2^((p-> add(ceil((p[j]-1)/2)

%p +add(igcd(p[k], p[j]), k=1..j-1), j=1..nops(p)))([l[], 1$n])),

%p add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i))

%p end:

%p a:= n-> n*b(n$2, []):

%p seq(a(n), n=1..20); # _Alois P. Heinz_, Aug 14 2019

%t Needs["Combinatorica`"];

%t Table[NumberOfGraphs[n]*n,{n,1,20}] (* _Geoffrey Critzer_, Oct 13 2012 *)

%Y Equals A000088(n)*n.

%Y Cf. A000169, A055543, A055544.

%K nonn

%O 1,2

%A _Eric W. Weisstein_

%E More terms from _Sascha Kurz_, Mar 25 2002