A055542 Total number of nodes in all simple graphs of n nodes.

1, 4, 12, 44, 170, 936, 7308, 98768, 2472012, 120051680, 11208976504, 1981094071104, 656526407783376, 406758179201296832, 471397289547064631520, 1024016251272440926318848, 4180909690610059855623236192, 32176399052621010609861807435264

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..87
• Eric Weisstein's World of Mathematics, Graph Vertex

Crossrefs

Equals A000088(n)*n.

Cf. A000169, A055543, A055544.

Programs

Maple

b:= proc(n, i, l) `if`(n=0 or i=1, 1/n!*2^((p-> add(ceil((p[j]-1)/2)
      +add(igcd(p[k], p[j]), k=1..j-1), j=1..nops(p)))([l[], 1$n])),
       add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i))
    end:
a:= n-> n*b(n$2, []):
seq(a(n), n=1..20);  # Alois P. Heinz, Aug 14 2019

Mathematica

Needs["Combinatorica`"];
Table[NumberOfGraphs[n]*n,{n,1,20}] (* Geoffrey Critzer, Oct 13 2012 *)

Extensions

More terms from Sascha Kurz, Mar 25 2002