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 A056164 #12 Feb 16 2025 08:32:43
%S A056164 1,2,6,109,191177
%N A056164 Number of ordered antichain covers of an unlabeled n-set; labeled T_1-hypergraphs (without empty hyperedges) with n hyperedges.
%C A056164 A T_1-hypergraph is a hypergraph (not necessarily without empty hyperedges or multiple hyperedges) which for every ordered pair of distinct nodes has a hyperedge containing one but not the other node.
%D A056164 V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
%D A056164 V. Jovovic and G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
%H A056164 K. S. Brown, <a href="http://www.mathpages.com/home/kmath515.htm">Dedekind's problem</a>
%H A056164 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Cover.html">Antichain covers</a>
%F A056164 a(n)=Sum_{k=1..C(n, floor(n/2))}b(k, n) where b(k, n) is the number of k-element ordered antichains covers of an unlabeled n-set.
%e A056164 There are 6 ordered antichain covers on an unlabeled 3-set: ({1,2,3}), ({1},{2,3}), ({2,3},{1}), ({1,2},{1,3}), ({1},{2},{3}), ({1,2},{1,3},{2,3}).
%e A056164 a(3)=1+3+2=6; a(4)=1+6+17+25+30+30=109; a(5)=1+10+71+429+2176+8310+20580+38640+60480+60480=191177.
%Y A056164 Cf. A056074, A056090, A056093, A000372, A056005, A056069-A056071, A056073, A056046-A056049, A056052, A056101, A056104, A051112-A051118.
%K A056164 hard,more,nonn
%O A056164 1,2
%A A056164 _Vladeta Jovovic_, Goran Kilibarda, Jul 31 2000