%I #24 Mar 01 2024 01:59:55
%S 1,1,2,5,20,180,16143,489996795,1392195548399980210,
%T 789204635842035039135545297410259322
%N Number of unlabeled simplicial complexes with n nodes.
%C Also the number of non-isomorphic antichains of nonempty sets covering n vertices. The labeled case is A006126, except with a(0) = 1. - _Gus Wiseman_, Feb 23 2019
%D Benoît Jubin, Posting to Sequence Fans Mailing List, Aug 12 2015.
%H C. Lienkaemper, A. Shiu, and Z. Woodstock, <a href="http://www.math.tamu.edu/~annejls/papers/obstructions-convexity-neural.pdf">Obstructions to convexity in neural codes</a>, Preprint 2015.
%H 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 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 First differences of A306505. - _Gus Wiseman_, Feb 23 2019
%F a(n) = A003182(n) - A003182(n-1) for n > 0. - _Andrew Howroyd_, May 28 2023
%e From _Gus Wiseman_, Feb 23 2019: (Start)
%e Non-isomorphic representatives of the a(0) = 1 through a(4) = 20 antichains:
%e {} {{1}} {{12}} {{123}} {{1234}}
%e {{1}{2}} {{1}{23}} {{1}{234}}
%e {{13}{23}} {{12}{34}}
%e {{1}{2}{3}} {{14}{234}}
%e {{12}{13}{23}} {{1}{2}{34}}
%e {{134}{234}}
%e {{1}{24}{34}}
%e {{1}{2}{3}{4}}
%e {{13}{24}{34}}
%e {{14}{24}{34}}
%e {{13}{14}{234}}
%e {{12}{134}{234}}
%e {{1}{23}{24}{34}}
%e {{124}{134}{234}}
%e {{12}{13}{24}{34}}
%e {{14}{23}{24}{34}}
%e {{12}{13}{14}{234}}
%e {{123}{124}{134}{234}}
%e {{13}{14}{23}{24}{34}}
%e {{12}{13}{14}{23}{24}{34}}
%e (End)
%Y Apart from a(0), same as A006602, and after subtracting 1, A007411.
%Y Cf. A000372, A003182, A006126, A014466, A261006, A304997, A304998, A306505, A306550, A321679.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Aug 13 2015
%E a(8)-a(9) added using A003182 by _Andrew Howroyd_, May 28 2023