I have 3 Integers, all three are entered by a user. With them I need to calculate how many possible permutations they are. I already got some code, it works fine for small integers, if they get bigger, my tool runs for literally days/hours? **Recursive function to calculate possible permutations:** def T(n, k, K): if k==0: return n==0 return sum(T(n-i, k-1, K) for i in xrange(0, K[k-1]+1)) **Explanation:** - n = Number of Bottles - k = Number of crates, - K = Maximum Number of possible Bottles one crate can fit K is different for each crate, and doesn't need to be full, it can even be empty. I'm calculating how many possibilities there are, to fit X given Bottles inside X given Crates, where one crate can fit a maximum of X Bottles. **Example for better Understanding:** Lets say, we have: - 7 Bottles *(n)* - 2 Crates *(k) -> [k1, k2]* - k1 fits 3 Bottles *(K1)*, k2 fits 5 Bottles *(K2)* *[k1 -> 3, k2 -> 5]* So they are **2** possibilities to fit the bottles inside the crates. Another one: - 7 Bottles *(n)* - 3 Crates *(k) -> [k1, k2, k3]* - k1 fits 2 Bottles, K2 fits 3 Bottles, K3 fits 4 Bottles **6** possibilities Above code calculates that flawless, but when I try it with like: **Problem:** - 30 Bottles (n) - 20 Crates (k) - k1 -> 1 Bottle *(K1)*, k2 -> 2 Bottles *(K2)*, k3 -> 3 Bottles *(K3)*, k4 -> 4 Bottles *(K4)*.. and so on until k20 -> 20 Bottles *(K20)*, im sure you get the idea.. It takes FOREVER, so I'm asking you; **Question:** How could I improve above code/function?