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 A124775 #4 Mar 30 2012 17:35:17 %S A124775 1,1,1,1,1,2,1,1,1,3,4,3,1,2,1,1 %N A124775 Number of unlabeled partially ordered sets associated with compositions in standard order. %C A124775 The standard order of compositions is given by A066099. %C A124775 The k-th term of the composition is the number of objects with rank k. The rank of an object is one more than the maximum rank of any smaller object in the ordering (1 for a minimal element), or equivalently the size of the largest chain of which the object is the maximal element. %e A124775 Composition number 11 is 2,1,1; there are 3 partial orders associated with this (shown below), so a(11) = 3. %e A124775 ..O..*O..*..O %e A124775 ..|..*|..*./| %e A124775 ..O..*O..*O.| %e A124775 ./.\.*|..*|.| %e A124775 O...O*O.O*O.O %e A124775 The table starts: %e A124775 1 %e A124775 1 %e A124775 1 1 %e A124775 1 2 1 1 %Y A124775 Cf. A066099, A124776, A124777, A011782 (row lengths), A000112 (row sums). %K A124775 more,nonn,tabf %O A124775 0,6 %A A124775 _Franklin T. Adams-Watters_, Nov 06 2006