|
%I #12 Jun 01 2018 01:54:26
%S 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 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 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 Number of set partitions associated with compositions in standard order.
%C The standard order of compositions is given by A066099.
%C 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 Alois P. Heinz, <a href="/A124772/b124772.txt">Rows n = 0..14, flattened</a>
%F For composition b(1),...,b(k), a(n) = Product_{i=1}^k C((Sum_{j=i}^k b(j))-1, b(i)-1).
%e 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 The table starts:
%e 1
%e 1
%e 1 1
%e 1 2 1 1
%Y Cf. A066099, A124773, A011782 (row lengths), A000110 (row sums), A036040, A080575.
%K easy,nonn,look,tabf
%O 0,6
%A _Franklin T. Adams-Watters_, Nov 06 2006
|
