Math Help - How can I solve this recursive relation?

1. How can I solve this recurrence relation?

$\\f(n, m) =\begin{cases}0, & \text{if }n,m < 0\\1, & \text{if }n,m = 0\\\sum_{i = 0}^{k = max(n, m)}([f(n - i, m - [k - i]) + c]\binom{k}{i}) - c(2^{k - 1} + 1), & \text{otherwise}\end{cases}$