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Algebra Level 5

Let P(x)P(x) be a polynomial of degree 99 satisfying P(n)=n99!P(n)=n \cdot 99! for n=1,2,3,,99n= 1,2,3,\ldots,99. If P(100)=0P(100)=0, find the value of the coefficient of x98x^{98} in P(x)P(x).

Notation: !! denotes the factorial notation. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .

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