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:

(define (multifactorial n d)
   (fold * 1 (iota (div n d) n (negate d))))

(for-each (lambda (i)
      (display "Degree ")
      (display i)
      (display ":")
      (for-each (lambda (n)
            (display " ")
            (display (multifactorial n i)))
         (iota 10 1))
      (print))
   (iota 5 1))


(define (!!!!! n) (multifactorial n 5))
(print (!!!!! 74))

(import (math infix-notation))
; register !!!!! as a postfix function
(define \\postfix-functions (put \\postfix-functions '!!!!! #t))

; now use "\\" as usual
(print (\\
   2 + 74!!!!!
))