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%I #11 Aug 04 2016 09:46:45
%S 1,2,7,52,851,28786,1933879,255839048,66839167987,34634544150646,
%T 35712147523562999,73426704068062929628,301419821377908100819123,
%U 2472253358027383404798964442,40532633024489540112983979301783,1328660090565074145503909701745941840
%N Number of simple labeled graphs G on n vertices such that for each k in {1,2,...,n}, G has exactly k connected components and the vertices labeled with {1,2,...,k} are all in different components.
%H Philippe Flajolet and Robert Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html">Analytic Combinatorics</a>, Cambridge Univ. Press, 2009, page 142.
%e a(3) = 7 because with 3 vertices there are four connected graphs, 1 2-3, 2 1-3, and the empty graph.
%t nn = 16; Map[Total,Map[Select[#, # > 0 &] &,Transpose[ Map[Take[#, nn] &,Table[Clear[g];g[z_] := Sum[2^Binomial[n, 2] z^n/n!, {n, 0, nn + k}]; Join[Table[0, {k - 1}], Range[0, nn]! CoefficientList[Series[D[Log[g[z]], z]^k, {z, 0, nn}], z]], {k, 1, nn}]]]]]
%Y Row sums of A275595.
%K nonn
%O 1,2
%A _Geoffrey Critzer_, Aug 03 2016
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