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Let \(\displaystyle a_n = n!(n+1)^2\) and \(\displaystyle S=\sum_{n=0}^{94} a_n\).

Find the remainder when \(S\) is divided by 97 .

Notation: \(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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