Problem Statement

The factorial of a number, written as

n !

{\displaystyle n!}

, is defined as

n !

n ( n − 1 ) ( n − 2 ) . . . ( 2 ) ( 1 )

{\displaystyle n!=n(n-1)(n-2)...(2)(1)}

. Multifactorials generalize factorials as follows: In all cases, the terms in the products are positive integers. If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:

Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.

Let's start with the solution:

main :: [sys_message]
main = [ Stdout (show deg ++ ": " ++ show (map (multifac deg) [1..10]) ++ "\n")
       | deg <- [1..5]]

multifac :: num->num->num
multifac deg = product . takewhile (>1) . iterate sub
               where sub n = n - deg