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 A330343 #7 Dec 14 2019 19:26:53 %S A330343 1,0,0,0,0,5760,766080,149022720,48990251520,28928242022400, %T A330343 32147584690636800,69035206021583155200 %N A330343 Number of labeled fully chiral simple graphs (also called identity or asymmetric graphs) covering n vertices. %C A330343 In a fully chiral graph, every permutation of the vertices gives a different representative, so the only automorphism is the identity. %F A330343 a(n) = n! * A003400(n). %t A330343 graprms[m_]:=Union[Table[Sort[Sort/@(m/.Rule@@@Table[{p[[i]],i},{i,Length[p]}])],{p,Permutations[Union@@m]}]]; %t A330343 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],Length[graprms[#]]==n!&]],{n,5}] (* brute force, not for computation *) %Y A330343 The unlabeled version is A003400. %Y A330343 Identity trees are A004111. %Y A330343 Covering simple graphs are A006129. %Y A330343 Full chiral integer partitions are A330228. %Y A330343 Fully chiral factorizations are A330235. %Y A330343 Fully chiral set-systems are A330229 (labeled covering), A330282 (labeled), A330294 (unlabeled), A330295 (unlabeled covering). %Y A330343 Graphs with exactly two automorphisms are A330297 (labeled covering), A330344 (unlabeled), A330345 (labeled), A330346 (unlabeled covering), A241454 (unlabeled connected). %Y A330343 Cf. A006125, A016031, A124059, A143543, A330098, A330224, A330226, A330227, A330230, A330231, A330236. %K A330343 nonn,more %O A330343 1,6 %A A330343 _Gus Wiseman_, Dec 12 2019