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

Author

Franklin T. Adams-Watters, Nov 06 2006

Keywords

• easy
• nonn
• tabf

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.

Examples

			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.

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)!.