recursive formula.

[BioGeek]

I'm trying to implement the following recursive formula in Perl:
''''''''''''''''''''''''''''''''''''_n
P(r₁,r₂,...,r_n) = Σ(r_n-i+1 - r_n-i)P(r₁,r₂,...,r_n-i,r_n-i+2,...,r_n)
'''''''''''''''''''''''''''''''''''ⁱ⁼¹

(if this doesn't render well, it is the second formula on this page),
where r₀=0 and the recursive call to P supplies all of the original arguments except the (n‑i+1)^th argument.
I've looked at Math::Sequence and Math::Series, but the examples given there are only for simple cases like
x_(n+1) = 1 / (x_n + 1)
and I'm a bit lost on how to implement this formula.

As sample data you can use:

r1	0,11	0,43	0,93	0,91	0,52
r2	0,07	0,31	0,78	0,12	0,18
r3	0,19	0,37	0,82	0,15	0,32

(which should give 5 P(r₁,r₂,...,r_n)-values)

Update: I've tried to work out a litlle example of the algorithm myself (but correct me If I'm doing something wrong).

P(r₁,r₂,r₃)= (r₃ - r₂)P(r₁,r₂) + (r₂ - r₁)P(r₁,r₃) + (r₁ - r₀)P(r₂,r₃)

Now the iteration comes into play, because to calculate the P-values in the rigth hand side of the formula, we use our original formula again.
P(r₁,r₂) = (r₂ - r₁)P(r₁) + (r₁ - r₀)P(r₂)
P(r₁,r₃) = (r₃ - r₁)P(r₁) + (r₁ - r₀)P(r₃)
P(r₂,r₃) = (r₃ - r₂)P(r₂) + (r₂ - r₀)P(r₃)

Update: the r-values are scores, and P is a probability:
so P(r₁) is the chance of having score r₁,
P(r₁,r₂) is the chance of both having score r₁ and score r₂,
and so on.