Superfactorial

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!