How to solve this sum of a recurrence relation?

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I've been given the recurrence relation $a_n = na_{n-1}+n^2a_{n-2}$ where $a_0 = 1$ and $a_1 = 1$.

I need to find $a_{1000}$.

My understanding is that this is very similar to the Fibonacci sequence. I also believe that I need to derive an explicit formula to find (And be able to express) the answer.

Unfortunately, I have zero idea how to do this and haven't found much that really helps me despite a long search.