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%I #28 Jun 07 2020 18:50:47
%S 0,1,2,9,75,1152,34682,2138198,269883034,68817253672,35198146897560,
%T 36032836311773232,73789380474381388000,302234317635238719436144,
%U 2475886860241348605928934912,40564851111492400113490251715664,1329228293742222434273523342085983312,87112291457022644126987794521680595912960
%N Number of ways to linearly order the components of a simple labeled graph on n nodes so that the label 1 is in the first component.
%F E.g.f.: Integral [d/dx log(g(x))]/(1 - log(g(x))) dx, where g(x) is the e.g.f. for A006125.
%t nn = 16; g[x_] := Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn+1}]; Table[n!, {n, 0, nn + 1}] CoefficientList[Integrate[Series[D[Log[g[x]], x]/(1 - Log[g[x]]), {x, 0, nn}], x], x]
%Y Cf. A006125, A335356.
%K nonn
%O 0,3
%A _Geoffrey Critzer_, Jun 04 2020