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%I #19 Sep 05 2019 02:41:10
%S 1,2,4,11,65,974,31744,2069971,267270041,68629753650,35171000942708,
%T 36024807353574291,73784587576805254665,302228602363365451957806,
%U 2475873310144021668263093216,40564787336902311168400640561099
%N The number of connected simple labeled graphs with <= n nodes.
%H G. C. Greubel, <a href="/A182100/b182100.txt">Table of n, a(n) for n = 0..80</a>
%F a(n) = Sum_{i=0..n} binomial(n,i)*A001187(i).
%F E.g.f.: exp(x)*A(x) where A(x) is e.g.f. for A001187.
%F a(n) = A327078(n) + n. - _Gus Wiseman_, Sep 03 2019
%e From _Gus Wiseman_, Sep 03 2019: (Start)
%e The a(0) = 1 through a(3) = 11 edge-sets (singletons represent uncovered vertices):
%e {} {} {} {}
%e {{1}} {{1}} {{1}}
%e {{2}} {{2}}
%e {{1,2}} {{3}}
%e {{1,2}}
%e {{1,3}}
%e {{2,3}}
%e {{1,2},{1,3}}
%e {{1,2},{2,3}}
%e {{1,3},{2,3}}
%e {{1,2},{1,3},{2,3}}
%e (End)
%t nn = 15; g = Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[Exp[x] (Log[g] + 1), {x, 0, nn}], x]
%Y The unlabeled version is A292300(n) + 1.
%Y Cf. A001187, A006129, A054592, A287689, A327070, A327075, A327078.
%K nonn
%O 0,2
%A _Geoffrey Critzer_, Apr 11 2012
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