# Extremely Deep Recursion - Part 1

The Ackermann function is a computable function which grows very, very quickly as its inputs grow. For example, while $$A(1,2),$$ $$A (2,2),$$ and $$A(3,2)$$ are equal to $$4,7,$$ and $$29,$$ respectively, $$A(4,2) \approx 2 \times 10^{19728}$$.

The Ackermann function can be defined as follows: $A(m,n) = \begin{cases} n+1 & \mbox{if } m = 0 \\ A(m-1, 1) & \mbox{if } m > 0 \mbox{ and } n = 0 \\ A(m-1, A(m, n-1)) & \mbox{if } m > 0 \mbox{ and } n > 0. \end{cases}$

What is the value of $$A(0,7)?$$

Details and assumptions

If you enjoyed this problem, you might also like Part 2 and Part 3.

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