factn1

Factn1 is a term sometimes used in mathematical texts and programming problems to denote a factorial-related function. In common usage, factn1(n) is defined as the factorial of n minus one, that is factn1(n) = (n−1)!, for integers n ≥ 1. This compact notation is introduced mainly for teaching or example purposes and is not part of a universally standardized notation.

The function is undefined for arguments outside its typical domain, though many authors extend the convention by defining 0! = 1, which yields factn1(1) = 0! = 1. Accordingly, the sequence produced by factn1(1), factn1(2), factn1(3), … begins as 1, 1, 2, 6, 24, and so on. Like the ordinary factorial, factn1(n) grows rapidly with n, and Stirling’s approximation can be applied to estimate its size: factn1(n) ≈ sqrt(2π(n−1)) ((n−1)/e)^(n−1).

Examples help illustrate its use: factn1(5) = 4! = 24, factn1(2) = 1, and factn1(1) = 1 under the usual 0! convention. While factn1 can simplify expressions in some problems, it is not a standard mathematical function and variations may exist in different texts.

See also: Factorial, Gamma function, Combinatorics.