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%I #9 Feb 27 2020 01:07:00
%S 1,1,2,8,61,979,32198,2089277,268307573,68716923913,35184302013572,
%T 36028793426712833,73786975811410580497,302231454743896729891579,
%U 2475880078460679602114069886,40564819207152522033364153642067,1329227995784508187140918633570844201
%N Number of simple labeled graphs on n nodes with at most one nontrivial acyclic component.
%F E.g.f.: exp(x)*exp(c(x) - t(x) )*(t(x) - x) where c(x) is the e.g.f. for A001187 and t(x) is the e.g.f. for A000272.
%t nn = 16; f[x_] := Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}]; a =
%t Range[0, nn]! CoefficientList[Series[ 1 + Log[f[x]], {x, 0, nn}], x];
%t c[x_] := Sum[a[[i]] x^(i - 1)/(i - 1)!, {i, 1, nn + 1}];
%t t[x_] := 1 + Sum[n^(n - 2) x^n/n!, {n, 1, nn}];
%t Range[0, nn]! CoefficientList[Series[Exp[x] Exp[c[x] - t[x]] (t[x] - x), {x, 0, nn}], x]
%Y Cf. A000272, A001187.
%K nonn
%O 0,3
%A _Geoffrey Critzer_, Feb 23 2020
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