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A307249 Number of simplicial complexes with n nodes.

%I A307249 #15 Mar 01 2024 02:00:08
%S A307249 1,1,2,9,114,6894,7785062,2414627396434,56130437209370320359966,
%T A307249 286386577668298410623295216696338374471993
%N A307249 Number of simplicial complexes with n nodes.
%C A307249 Except for a(0) = 1, this is also the number of antichains of nonempty sets covering n vertices (A006126). There are two antichains of size zero, namely {} and {{}}, while there is only one simplicial complex, namely {}. The unlabeled case is A261005. The non-covering case is A014466.
%H A307249 Francisco Ponce Carrión and Seth Sullivant, <a href="https://arxiv.org/abs/2402.16292">Marginal Independence and Partial Set Partitions</a>, arXiv:2402.16292 [math.ST], 2024. See p. 21.
%H A307249 Gus Wiseman, <a href="/A048143/a048143_4.txt">Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons</a>.
%F A307249 Inverse binomial transform of A014466.
%e A307249 Maximal simplices of the a(0) = 1 through a(3) = 9 simplicial complexes:
%e A307249   {}    {{1}}  {{12}}    {{123}}
%e A307249                {{1}{2}}  {{1}{23}}
%e A307249                          {{2}{13}}
%e A307249                          {{3}{12}}
%e A307249                          {{12}{13}}
%e A307249                          {{12}{23}}
%e A307249                          {{13}{23}}
%e A307249                          {{1}{2}{3}}
%e A307249                          {{12}{13}{23}}
%t A307249 nn=5;
%t A307249 stableSets[u_,Q_]:=If[Length[u]===0,{{}},With[{w=First[u]},Join[stableSets[DeleteCases[u,w],Q],Prepend[#,w]&/@stableSets[DeleteCases[u,r_/;r===w||Q[r,w]||Q[w,r]],Q]]]];
%t A307249 Table[Length[stableSets[Subsets[Range[n],{2,n}],SubsetQ]],{n,0,nn}]
%Y A307249 Cf. A000372, A003182, A006126, A006602, A014466, A261005, A293606, A293993, A305000, A305844, A306550, A317674, A319721, A320449.
%K A307249 nonn,more
%O A307249 0,3
%A A307249 _Gus Wiseman_, Mar 31 2019
%E A307249 a(9) from _Dmitry I. Ignatov_, Nov 25 2023