# My Eleventh Problem

Algebra Level 5

Let $$n\in\mathbb{N}$$ and $$f(0)=1$$.

Simplify $$f$$ for:

$$f(n)=k^{n}+\sum_{a=1}^{n}[mk^{a-1}\times(k^{n-a}+\sum_{b=1}^{n-a}[mk^{b-1}\times(k^{n-a-b}+\sum_{c=1}^{n-a-b}[mk^{c-1}\times(k^{n-a-b-c}+\sum_{d=1}^{n-a-b-c}[... ...])])])]$$

for arbitrary constants $$k$$ and $$m$$, where $$f$$ is a function of a natural number or $$0$$.

×