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

%I A055542 #20 Feb 16 2025 08:32:43
%S A055542 1,4,12,44,170,936,7308,98768,2472012,120051680,11208976504,
%T A055542 1981094071104,656526407783376,406758179201296832,
%U A055542 471397289547064631520,1024016251272440926318848,4180909690610059855623236192,32176399052621010609861807435264
%N A055542 Total number of nodes in all simple graphs of n nodes.
%H A055542 Alois P. Heinz, <a href="/A055542/b055542.txt">Table of n, a(n) for n = 1..87</a>
%H A055542 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphVertex.html">Graph Vertex</a>
%p A055542 b:= proc(n, i, l) `if`(n=0 or i=1, 1/n!*2^((p-> add(ceil((p[j]-1)/2)
%p A055542       +add(igcd(p[k], p[j]), k=1..j-1), j=1..nops(p)))([l[], 1$n])),
%p A055542        add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i))
%p A055542     end:
%p A055542 a:= n-> n*b(n$2, []):
%p A055542 seq(a(n), n=1..20);  # _Alois P. Heinz_, Aug 14 2019
%t A055542 Needs["Combinatorica`"];
%t A055542 Table[NumberOfGraphs[n]*n,{n,1,20}] (* _Geoffrey Critzer_, Oct 13 2012 *)
%Y A055542 Equals A000088(n)*n.
%Y A055542 Cf. A000169, A055543, A055544.
%K A055542 nonn
%O A055542 1,2
%A A055542 _Eric W. Weisstein_
%E A055542 More terms from _Sascha Kurz_, Mar 25 2002