How to solve this recurrence relation with a summation in it?

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How would one go about solving this recurrence relation: $T(n)$=$\sum_{i=1}^{k}T(n - d_i)$ ?

For this recurrence relation, $k$ is the number of coin denominations, and $d_i$ is the specific coin denomination. I have stared at this for a while and have no idea how to go about it.

Thanks