

A124773


Number of permutations associated with compositions in standard order.


3



1, 1, 1, 1, 2, 2, 1, 1, 6, 6, 3, 3, 2, 2, 1, 1, 24, 24, 12, 12, 8, 8, 4, 4, 6, 6, 3, 3, 2, 2, 1, 1, 120, 120, 60, 60, 40, 40, 20, 20, 30, 30, 15, 15, 10, 10, 5, 5, 24, 24, 12, 12, 8, 8, 4, 4, 6, 6, 3, 3, 2, 2, 1, 1, 720, 720, 360, 360, 240, 240, 120, 120, 180, 180, 90, 90, 60, 60, 30
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OFFSET

0,5


COMMENTS

The standard order of compositions is given by A066099.
Arrange the cycles of the permutation by the smallest member of each cycle and read off the cycle sizes. E.g., for (1)(24)(3), the associated composition is 1,2,1.


LINKS



FORMULA

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


EXAMPLE

Composition number 11 is 2,1,1; the associated permutations are (12)(3)(4), (13)(2)(4) and (14)(2)(3), so a(11) = 3.
The table starts:
1
1
1 1
2 2 1 1


CROSSREFS



KEYWORD

easy,nonn,tabf


AUTHOR



STATUS

approved



