A124773 Number of permutations associated with compositions in standard order.

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

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

Table of n, a(n) for n=0..78.

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

Cf. A066099, A124772, A124774, A011782 (row lengths), A000142 (row sums), A036039.

Sequence in context: A141760 A114626 A221916 * A129177 A127452 A263755

Adjacent sequences: A124770 A124771 A124772 * A124774 A124775 A124776

Keyword

easy,nonn,tabf

Author

Franklin T. Adams-Watters, Nov 06 2006

Status

approved