

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
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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 1243, 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 1243 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 1234, 1324 and 1423, 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 A079415 A126347
Adjacent sequences: A124769 A124770 A124771 * A124773 A124774 A124775


KEYWORD

easy,nonn,look,tabf


AUTHOR

Franklin T. AdamsWatters, Nov 06 2006


STATUS

approved



