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Wikipedia definition
1. Alternating factorialIn mathematics, an alternating factorial is the absolute value of the alternating sum of the first n factorials. This is the same as their sum, with the odd-indexed factorials multiplied by −1 if n is even, and the even-indexed factorials multiplied by −1 if n is odd, resulting in an alternation of signs of the summands (or alternation of addition and subtraction operators, if preferred). To put it algebraically, or with the recurrence relation in which af(1) = 1.
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