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 A156235 #10 Dec 12 2015 04:31:09
%S A156235 1,1,4,198,209342
%N A156235 Number of irreflexive binary relations on the power set P(N) of an n-element set N as restricted below.
%C A156235 Each enumerated irreflexive relation R has these restricting properties:
%C A156235 Let (A,B) and (C,D) be arbitrary elements of R. Then
%C A156235 i) A and B are nonempty subsets of N,
%C A156235 ii) A and B are disjoint, and
%C A156235 iii) if (A,B) is not equal to (C,D) and A intersect C is nonempty, then B and D are disjoint.
%C A156235 Each a(n) includes the empty relation. Each relation R may contain any number of elements from 0 to n^2-n.
%C A156235 Inspired by considering less-restricted gift-exchange scenarios than in A053763.
%C A156235 Essentially, the scenarios here relax (somewhat but not entirely) noted restrictions iii) and iv) given there to allow joint giving and joint receiving.
%C A156235 More generally, these relations could be considered distribution networks (or even possible economies, in some sense) for goods and/or services whenever an entity cannot directly distribute to itself or to another entity of which it is a part and whenever an entity cannot (jointly) distribute directly to a second entity in more than one way (e.g., as part of two larger entities).
%e A156235 One of the 209342 irreflexive relations corresponding to a(4) is
%e A156235 R = {({1},{2}), ({2},{1}), ({3,4},{1,2}), ({1,4},{3}), ({2},{3,4})}.
%e A156235 Notice how the last three ordered pairs correspond to jointly giving and/or receiving gifts.
%Y A156235 Cf. A000392, A002378, A028243, A053763.
%K A156235 nonn,more
%O A156235 0,3
%A A156235 _Rick L. Shepherd_, Feb 06 2009