Ordered partitions

Example. The partitions of 5 are:
5
4 1
3 2
3 1 1
2 2 1
2 1 1 1
1 1 1 1 1

The -ordered- partitions of 5 are:
5
4 1
1 4
3 2
2 3
3 1 1
1 3 1
1 1 3
2 2 1
2 1 2
1 2 2
2 1 1 1
1 2 1 1
1 1 2 1
1 1 1 2
1 1 1 1 1

Note:
1 ( of 1 ) = C(4,0)
4 ( of 2 ) = C(4,1)
6 ( of 3 ) = C(4,2)
4 ( of 4 ) = C(4,3)
1 ( of 5 ) = C(4,4)

The number of ordered partitions of n = 2^(n-1). In the case of 5: 2^4=16.

Try 3,4 or 6 as an ( interesting ) exercise.