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%I #9 Feb 23 2013 06:37:11
%S 1,1,1,3,8,29,142,1005,12173,273582,11992634,1018722089,165079154766,
%T 50501012094102,29053990554043728,31426435466753662607,
%U 64000986650206797417763,245935832726996459827917035,1787577661144566941699523416191,24637809007189108944313598892070582
%N The number of unlabelled simple graphs with n nodes such that no two connected components are identical.
%F O.g.f.: Product_{n >=1} (1+x^n)^A001349(n) where A001349 is the number of connected graphs.
%e a(4)=8 because there are eleven graphs with 4 nodes but three have (at least two) components that are identical: * * * * , *-* *-* , * * *-*
%t nn=19;a={1,1,2,6,21,112,853,11117,261080,11716571,1006700565,164059830476,50335907869219,29003487462848061,31397381142761241960,63969560113225176176277,245871831682084026519528568,1787331725248899088890200576580,24636021429399867655322650759681644};CoefficientList[Series[Product[(1+x^i)^a[[i]],{i,1,nn}],{x,0,nn}],x]
%K nonn
%O 0,4
%A _Geoffrey Critzer_, Feb 20 2012
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