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$$\sum_{n=0}^{\infty} \frac{n^3((2n)!) + (2n-1)(n!)}{(n!)(2n)!} = ae + \frac{b}{e} + c$$ where $$a, b, c \in \mathbb{Z}$$ and $$e = \sum_{n=0}^{\infty} \frac{1}{n!}$$. Then $$a^2 - b + c$$ is equal to ______.
Correct Answer: 26
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