A124772 Number of set partitions associated with compositions in standard order.

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, 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, 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

Offset

0,6

Comments

The standard order of compositions is given by A066099.

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}.

Links

Alois P. Heinz, Rows n = 0..14, flattened

Formula

For composition b(1),...,b(k), a(n) = Product_{i=1}^k C((Sum_{j=i}^k b(j))-1, b(i)-1).

Example

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.
The table starts:
1
1
1 1
1 2 1 1

Crossrefs

Cf. A066099, A124773, A011782 (row lengths), A000110 (row sums), A036040, A080575.

Sequence in context: A292745 A047010 A047100 * A227543 A366920 A344678

Adjacent sequences: A124769 A124770 A124771 * A124773 A124774 A124775

Keyword

easy,nonn,look,tabf

Author

Franklin T. Adams-Watters, Nov 06 2006

Status

approved