Figure-It-Out Function! - Part 3: The Powers of Factorials

Algebra Level 4

Let there be a function \(f(x):\mathbb{Z}\rightarrow \mathbb{Z}\) with the following conditions

\[ \begin{cases}{f(x+1)=f(x)+(f(x))!} \\ {f(3)=28}\end{cases} \]

Evaluate \(\displaystyle \sum_{i=-1}^{4} \left [ f(i) \cdot f(3-i) \right ] \)

This problem is part of the Figure-It-Out Function! series.
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