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 A124772 #12 Jun 01 2018 01:54:26
%S A124772 1,1,1,1,1,2,1,1,1,3,3,3,1,2,1,1,1,4,6,6,4,8,4,4,1,3,3,3,1,2,1,1,1,5,
%T A124772 10,10,10,20,10,10,5,15,15,15,5,10,5,5,1,4,6,6,4,8,4,4,1,3,3,3,1,2,1,
%U A124772 1,1,6,15,15,20,40,20,20,15,45,45,45,15,30,15,15,6,24,36,36,24,48,24,24,6,18
%N A124772 Number of set partitions associated with compositions in standard order.
%C A124772 The standard order of compositions is given by A066099.
%C A124772 Arrange the parts of the set partition by the smallest member of each part and read off the part sizes. E.g., for 1|24|3, the associated composition is 1,2,1. When the set partition is presented as the sequence of parts that each member is in, simply count the times each part number occurs. This representation for 1|24|3 is {1,2,3,2}.
%H A124772 Alois P. Heinz, <a href="/A124772/b124772.txt">Rows n = 0..14, flattened</a>
%F A124772 For composition b(1),...,b(k), a(n) = Product_{i=1}^k C((Sum_{j=i}^k b(j))-1, b(i)-1).
%e A124772 Composition number 11 is 2,1,1; the associated set partitions are 12|3|4, 13|2|4 and 14|2|3, so a(11) = 3.
%e A124772 The table starts:
%e A124772 1
%e A124772 1
%e A124772 1 1
%e A124772 1 2 1 1
%Y A124772 Cf. A066099, A124773, A011782 (row lengths), A000110 (row sums), A036040, A080575.
%K A124772 easy,nonn,look,tabf
%O A124772 0,6
%A A124772 _Franklin T. Adams-Watters_, Nov 06 2006