Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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