The term "superfactorial" is used to refer to an extension of the factorial function, similar to how tetration is an extension of exponentiation. The superfactorial of a positive integer \( n \) is denoted as \( \text{sf}(n) \) and is defined as the product of the factorials of all positive integers up to \( n \). Mathematically, it is defined as: \[ \text{sf}(n) = 1!
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The superfactorial of a nonnegative integer is the product . This convention differs from other similarly named iterated factorial operations, so the product definition should be stated.