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 A381472 #6 Mar 05 2025 15:08:12
%S A381472 1,2,5,22,345,152589
%N A381472 Number of unlabeled set systems on n vertices which are closed under union of disjoint sets.
%C A381472 A set system is a finite set of finite nonempty sets.
%C A381472 a(n) is also the number of non-isomorphic sets of subsets of an n-set which are closed under union of disjoint sets and which include the empty set.
%e A381472 Non-isomorphic representatives of the a(2) = 5 set-systems:
%e A381472 {}
%e A381472 {{1}}
%e A381472 {{1,2}}
%e A381472 {{1},{1,2}}
%e A381472 {{1},{2},{1,2}}
%e A381472 The a(3) = 22 non-isomorphic set-systems include A193674(3) = 19 set-systems that are closed under union and 3 additional set-systems which do not include {1,2,3}:
%e A381472 {{1,2},{1,3}}
%e A381472 {{1},{1,2},{1,3}}
%e A381472 {{1,2},{1,3},{2,3}}
%Y A381472 Cf. A000612 (set-systems), A193674 (closed under union of sets), A381471, A381575 (labeled case).
%K A381472 nonn,hard,more
%O A381472 0,2
%A A381472 _Andrew Howroyd_, Mar 02 2025