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%I #11 Jun 16 2017 22:27:26
%S 0,1,3,7,19,55,222,1303,13845,289796,12309107,1031600490,166135132131,
%T 50669199124597,29104991031790932,31455641633255556350,
%U 64032500451659605651790,245999928109779646497947269,1787823789106309664923287885113
%N Number of connected components over all simple unlabeled graphs with n nodes.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedComponent.html">Connected Component</a>
%F Sum_{m=1..n} A201922(m,n).
%t nn=15; f[list_] := Total[Table[list[[i]]*(i-1), {i,1,Length[list]}]]; g[x_]:=Sum[NumberOfGraphs[n]x^n,{n,0,nn}]; c[x_]:=Sum[a[n]x^n,{n,0,nn}]; a[0]=1; sol=SolveAlways[g[x]==Normal[Series[Product[1/(1-x^i)^a[i], {i,1,nn}], {x,0,nn}]], x]; b=Drop[Flatten[Table[a[n],{n,0,nn}]/.sol],1]; Map[f,CoefficientList[Series[Product[1/(1-y x^i)^b[[i]], {i,1,nn}], {x,0,nn}], {x,y}]]
%K nonn
%O 0,3
%A _Geoffrey Critzer_, Mar 30 2013
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