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 A072445 #17 Oct 28 2023 15:27:47
%S A072445 1,1,1,4,40,3044,26894586
%N A072445 Number of subsets S of the power set P{1,2,...,n} such that: {1}, {2},..., {n} are all elements of S; {1,2,...,n} is an element of S; if X and Y are elements of S and X and Y have a nonempty intersection, then the union of X and Y is an element of S. The sets S are counted modulo permutations on the elements 1,2,...,n.
%C A072445 We define a connectedness system to be a set of finite nonempty sets (edges) that is closed under taking the union of any two overlapping edges. It is connected if it is empty or contains an edge with all the vertices. Then a(n) is the number of unlabeled connected connectedness systems without singletons on n vertices. - _Gus Wiseman_, Aug 01 2019
%H A072445 Wim van Dam, <a href="http://www.cs.berkeley.edu/~vandam/subpowersets/sequences.html">Sub Power Set Sequences</a>
%H A072445 Gus Wiseman, <a href="/A072445/a072445.txt">Non-isomorphic representatives of the a(4) = 40 connected connectedness systems without singletons.</a>
%F A072445 Inverse Euler transform of A072444. - _Andrew Howroyd_, Oct 28 2023
%e A072445 a(3) = 4 because of the 4 sets: {{1}, {2}, {3}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 3}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}.
%Y A072445 The non-connected case is A072444.
%Y A072445 The labeled case is A072447.
%Y A072445 The case with singletons is A326869.
%Y A072445 Cf. A072446, A092918, A108798, A326866, A326867, A326871, A326879.
%K A072445 nonn,more
%O A072445 0,4
%A A072445 Wim van Dam (vandam(AT)cs.berkeley.edu), Jun 18 2002
%E A072445 a(0)=1 prepended and a(6) corrected by _Andrew Howroyd_, Oct 28 2023