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
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
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)!.
Comments