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A124772
Number of set partitions associated with compositions in standard order.
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
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
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 A374932
KEYWORD
easy,nonn,look,tabf
AUTHOR
STATUS
approved