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 A380571 #33 Mar 02 2025 23:22:17
%S A380571 1,1,2,5,19,137,3708,1506404,230328505024
%N A380571 Number of Dynkin systems on [n].
%C A380571 A Dynkin system on a set S is a subset of the power set of S which contains the empty set, is closed under complements in S, and is closed under union of disjoint sets.
%H A380571 Martin Rubey and Peter Taylor, <a href="https://mathoverflow.net/q/405736/46140">What is the number of finite Dynkin systems?</a>, MathOverflow.
%H A380571 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dynkin_system">Dynkin system</a>
%F A380571 a(n) >= A000110(n).
%e A380571 The a(3) = 5 systems are:
%e A380571 {{}, {1,2,3}}
%e A380571 {{}, {1}, {2,3}, {1,2,3}}
%e A380571 {{}, {2}, {1,3}, {1,2,3}}
%e A380571 {{}, {3}, {1,2}, {1,2,3}}
%e A380571 {{}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}}
%e A380571 The a(4) = 19 systems are 15 sigma-algebras counted by A000110(4) and 4 other systems:
%e A380571 {{}, {1,2,3,4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}}
%e A380571 {{}, {1,2,3,4}, {1,2}, {1,3}, {2,4}, {3,4}}
%e A380571 {{}, {1,2,3,4}, {1,2}, {1,4}, {2,3}, {3,4}}
%e A380571 {{}, {1,2,3,4}, {1,3}, {1,4}, {2,3}, {2,4}}
%Y A380571 Cf. A000110, A102894, A381471 (unlabeled case).
%K A380571 nonn,hard,more
%O A380571 0,3
%A A380571 _Peter J. Taylor_, Feb 24 2025