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%I #39 Dec 19 2023 13:41:18
%S 1,1,3,14,165,14480,108281182,2796163091470050
%N Number of nonisomorphic systems enumerated by A102894; that is, the number of inequivalent closure operators in which the empty set is closed. Also, the number of union-closed sets with n elements that contain the universe and the empty set.
%C Also the number of unlabeled finite sets of subsets of {1..n} that contain {} and {1..n} and are closed under intersection. - _Gus Wiseman_, Aug 02 2019
%H Maria Paola Bonacina and Nachum Dershowitz, <a href="https://doi.org/10.1007/978-3-642-37651-1_3">Canonical ground Horn theories</a>, Lecture Notes in Computer Science 7797, 35-71 (2013).
%H G. Brinkmann and R. Deklerck, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL21/Brinkmann/brink6.html">Generation of Union-Closed Sets and Moore Families</a>, Journal of Integer Sequences, Vol.21 (2018), Article 18.1.7.
%H G. Brinkmann and R. Deklerck, <a href="https://arxiv.org/abs/1701.03751">Generation of Union-Closed Sets and Moore Families</a>, arXiv:1701.03751 [math.CO], 2017.
%H Christopher S. Flippen, <a href="https://scholarscompass.vcu.edu/etd/7527/">Minimal Sets, Union-Closed Families, and Frankl's Conjecture</a>, Master's thesis, Virginia Commonwealth Univ., 2023.
%F a(n) = A108800(n)/2.
%e From _Gus Wiseman_, Aug 02 2019: (Start)
%e Non-isomorphic representatives of the a(0) = 1 through a(3) = 14 union-closed sets of sets:
%e {} {}{1} {}{12} {}{123}
%e {}{2}{12} {}{3}{123}
%e {}{1}{2}{12} {}{23}{123}
%e {}{1}{23}{123}
%e {}{3}{23}{123}
%e {}{13}{23}{123}
%e {}{2}{3}{23}{123}
%e {}{2}{13}{23}{123}
%e {}{3}{13}{23}{123}
%e {}{12}{13}{23}{123}
%e {}{2}{3}{13}{23}{123}
%e {}{3}{12}{13}{23}{123}
%e {}{2}{3}{12}{13}{23}{123}
%e {}{1}{2}{3}{12}{13}{23}{123}
%e (End)
%Y The labeled version is A102894.
%Y Cf. A000612, A001930, A003180, A102895, A102897, A108800, A193674, A193675, A326867, A326869, A326883.
%K nonn,more
%O 0,3
%A _Don Knuth_, Jul 01 2005
%E a(6) added (using A193674) by _N. J. A. Sloane_, Aug 02 2011
%E Added a(7), and reference to union-closed sets. - _Gunnar Brinkmann_, Feb 05 2018