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 A124777 #5 Mar 30 2012 17:35:17 %S A124777 1,1,1,1,1,4,1,1,1,11,13,8,1,4,1,1 %N A124777 Number of naturally labeled partially ordered sets associated with compositions in standard order. %C A124777 The standard order of compositions is given by A066099. %C A124777 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 A124777 Composition number 11 is 2,1,1; there are 3 partial orders %e A124777 associated with this (shown below); these can be naturally labeled %e A124777 respectively in 1, 4 and 3 ways, so a(11) = 1+4+3 = 8. %e A124777 ..O..*O..*..O %e A124777 ..|..*|..*./| %e A124777 ..O..*O..*O.| %e A124777 ./.\.*|..*|.| %e A124777 O...O*O.O*O.O %e A124777 The table starts: %e A124777 1 %e A124777 1 %e A124777 1 1 %e A124777 1 4 1 1 %Y A124777 Cf. A066099, A124775, A124776, A011782 (row lengths), A006455 (row sums). %K A124777 more,nonn,tabf %O A124777 0,6 %A A124777 _Franklin T. Adams-Watters_, Nov 06 2006