Number of possible sequence partitioning

Question

Given a sequence of 1 and 0 elements, what is the number of possible partitioning of the sequence in sub-sequences (not necessarily consecutive elements, and any number of sub-sequences are allowed) so that any sub-sequence starts and ends with a 1, and can contain an arbitrary number of 0s?

For example: Given the sequence 1 0 1 1 0 1 there are only 3 ways of partitioning the sequence:

1.
1 0 1
      1 0 1

2.
1 0     0 1
    1 1

3.
1 0   1
    1   0 1

I am pretty sure the solution implies dynamic programming, since the solution requires a fast execution time (< 1 second).