# My problems #7

Algebra Level 5

Define the function $$f(n)$$ where $$n$$ is a nonnegative integer satisfying $$f(0) = 1$$ and $$f(n)$$ is defined for $$n>0$$ as $$f(n) = n\times{\displaystyle\sum_{i=0}^{n-1}\ f(i)}$$.

Let $$2^k$$ be the highest power of 2 that divides $$f(20)$$. Find $$\sqrt{ 2^k}$$.

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