This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A189831 #18 Sep 08 2022 08:45:56
%S A189831 0,0,0,4,85,1707,37457,921896,25477371,786163135,26890701739,
%T A189831 1012165431744,41638805754078,1860589088529164,89802422444553825,
%U A189831 4658465562594667088,258566755450911870007,15294477441385413149679,960641026388207044487891,63861339527473864490450300
%N A189831 Labeled simple graphs with n nodes and n-1 edges that are not trees.
%C A189831 Equivalently a(n) is the number of labeled simple graphs on n nodes having n-1 edges that have at least two connected components.
%C A189831 Evidently almost all such graphs are disconnected.
%H A189831 G. C. Greubel, <a href="/A189831/b189831.txt">Table of n, a(n) for n = 1..370</a>
%F A189831 a(n) = C(C(n,2),n-1) - n^(n-2) = A014068(n-1)-A000272(n), where C(x,y) is the binomial coefficient.
%e A189831 a(4) = 4 because there are 20 labeled simple graphs on four nodes with three edges but 16 of these are connected i.e. they are trees.
%t A189831 Table[Binomial[Binomial[n,2],n-1]-n^(n-2),{n,1,20}]
%o A189831 (PARI) for(n=1,20, print1(binomial(binomial(n,2),n-1) - n^(n-2), ", ")) \\ _G. C. Greubel_, Jan 14 2018
%o A189831 (Magma) [Binomial(Binomial(n,2),n-1) - n^(n-2): n in [1..20]]; // _G. C. Greubel_, Jan 14 2018
%Y A189831 Cf. A084546, A000272, A014068.
%K A189831 nonn
%O A189831 1,4
%A A189831 _Geoffrey Critzer_, Apr 28 2011