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 A369143 #12 Feb 02 2024 19:29:35
%S A369143 0,0,0,0,0,30,1335,47460,1651230,59636640,2284113762,93498908580,
%T A369143 4099070635935,192365988161490,9646654985111430,515736895712230192,
%U A369143 29321225548502776980,1768139644819077541440,112805126206185257070660,7595507651522103787077270,538504704005397535690160274
%N A369143 Number of labeled simple graphs with n edges and n vertices such that it is not possible to choose a different vertex from each edge (non-choosable).
%H A369143 Andrew Howroyd, <a href="/A369143/b369143.txt">Table of n, a(n) for n = 0..200</a>
%F A369143 a(n) = A116508(n) - A137916(n). - _Andrew Howroyd_, Feb 02 2024
%e A369143 The term a(5) = 30 counts all permutations of the graph {{1,2},{1,3},{1,4},{2,3},{2,4}}.
%t A369143 Table[Length[Select[Subsets[Subsets[Range[n],{2}], {n}],Length[Select[Tuples[#],UnsameQ@@#&]]==0&]],{n,0,5}]
%Y A369143 The version without the choice condition is A116508, covering A367863.
%Y A369143 The complement is A137916.
%Y A369143 Allowing any number of edges gives A367867, covering A367868.
%Y A369143 The version with loops is A368596, covering A368730, unlabeled A368835.
%Y A369143 For set-systems we have A368600, for any number of edges A367903.
%Y A369143 The covering case is A369144.
%Y A369143 A006125 counts simple graphs, unlabeled A000088.
%Y A369143 A058891 counts set-systems (without singletons A016031), unlabeled A000612.
%Y A369143 Cf. A000085, A057500, A062740, A129271, A133686, A333331, A367769, A367869, A367901, A367907.
%K A369143 nonn
%O A369143 0,6
%A A369143 _Gus Wiseman_, Jan 21 2024
%E A369143 a(8) onwards from _Andrew Howroyd_, Feb 02 2024