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%I #7 Jan 18 2016 21:28:43
%S 0,1,3,19,219,4691,188215,14388823,2128027015,615859881223,
%T 351128005027151,395921495115621487,885006516085472323279,
%U 3928043932547284205971407,34658076266993991201736109023,608435086028952410310283975943071
%N Total number of nodes in a maximal connected component over all simple labeled graphs on n nodes.
%C In other words, a(n) is the total number of nodes in one maximal component of each of the graphs in A006125.
%t nn = 15; a = Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}]; b =
%t Total[(Range[0, nn]! CoefficientList[Series[ Log[a], {x, 0, nn}],
%t x]) Table[x^i/i!, {i, 0, nn}]]; Map[Total,Transpose[
%t Table[Range[0, nn]! CoefficientList[Series[n (Exp[b[[1 ;; n]]] - Exp[b[[1 ;; n - 1]]]), {x, 0, nn}], x], {n, 1, nn}]]]
%Y Cf. A006125.
%K nonn
%O 0,3
%A _Geoffrey Critzer_, Jan 18 2016
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