|
Search: id:A124772
|
|
|
| A124772 |
|
Number of set partitions associated with compositions in standard order. |
|
+0
2
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
0,6
|
|
|
COMMENT
|
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 number of times each part number occurs. This representation for 1|24|3 is {1,2,3,2}.
|
|
FORMULA
|
For composition b(1),...,b(k), a(n) = Product_{i=1}^n C((Sum_{j=i}^n 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.
Adjacent sequences: A124769 A124770 A124771 this_sequence A124773 A124774 A124775
Sequence in context: A118923 A047010 A047100 this_sequence A079415 A126347 A057001
|
|
KEYWORD
|
easy,nonn,tabf
|
|
AUTHOR
|
Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 06 2006
|
|
|
Search completed in 0.002 seconds
|
