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:

' FB 1.05.0 Win64

Function multiFactorial (n As UInteger, degree As Integer) As UInteger
  If  n < 2 Then Return 1
  Var result = n
  For i As Integer = n - degree To 2 Step -degree
    result *= i
  Next
  Return result
End Function

For degree As Integer = 1 To 5
  Print "Degree"; degree; " => ";
  For n As Integer = 1 To 10
    Print multiFactorial(n, degree); " ";
  Next n
  Print 
Next degree

Print
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