I’m an actuarie, so I’m thinking in an insurance related way it could they have some use. Imagine a re insurance contract (the insurance that insurance companies buy to protect themselves) that pay after an S = sum Xi value of cumulative claims is reached (i = 1, 2, 3… number of claims, X = value of each claim) . How many ways can S be reached, given that they are N claims, with variable X?

For example, S = 4, that value can be reached by X = 4, X1= 3 + X2 = 1, and so on. Knowing the number of ways you can reach that S value, can help you with the pricing of the contract, or forecasting to when the S value is going to be reached.

Other than that, they are distributed computer power, if you need S computer power, how many ways can this value be reached knowing that you have access to N GPUs each one with Xi capacity.