What is the maximum recursion depth in Python, and how to increase it?

It is a guard against a stack overflow, yes. Python (or rather, the CPython implementation) doesn't optimize tail recursion, and unbridled max recursion depth python causes stack overflows. You can change the recursion limit with sys.setrecursionlimit, but doing so is risky -- the standard limit is a little conservative, but Python stack frames can be quite big.

Python isn't a functional language and tail recursion is not a particularly efficient technique. Rewriting the algorithm iteratively, if possible, is generally a better idea.