 Superfactorial

The superfactorial of a nonnegative integer $n$ is the product ${\prod }_{k=1}^{n}k!$. This convention differs from other similarly named iterated factorial operations, so the product definition should be stated.

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!