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:

 



n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)


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


 



n
!
!
=
n
(
n
−
2
)
(
n
−
4
)
.
.
.


{\displaystyle n!!=n(n-2)(n-4)...}


 



n
!
!
!
=
n
(
n
−
3
)
(
n
−
6
)
.
.
.


{\displaystyle n!!!=n(n-3)(n-6)...}


 



n
!
!
!
!
=
n
(
n
−
4
)
(
n
−
8
)
.
.
.


{\displaystyle n!!!!=n(n-4)(n-8)...}


 



n
!
!
!
!
!
=
n
(
n
−
5
)
(
n
−
10
)
.
.
.


{\displaystyle n!!!!!=n(n-5)(n-10)...}


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:

 Write a function that given n and the degree, calculates the multifactorial.
 Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial.

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

namespace RosettaCode.Multifactorial
{
    using System;
    using System.Linq;
 
    internal static class Program
    {
        private static void Main()
        {
            Console.WriteLine(string.Join(Environment.NewLine,
                                          Enumerable.Range(1, 5)
                                                    .Select(
                                                        degree =>
                                                        string.Join(" ",
                                                                    Enumerable.Range(1, 10)
                                                                              .Select(
                                                                                  number =>
                                                                                  Multifactorial(number, degree))))));
        }
 
        private static int Multifactorial(int number, int degree)
        {
            if (degree < 1)
            {
                throw new ArgumentOutOfRangeException("degree");
            }
 
            var count = 1 + (number - 1) / degree;
            if (count < 1)
            {
                throw new ArgumentOutOfRangeException("number");
            }
 
            return Enumerable.Range(0, count)
                             .Aggregate(1, (accumulator, index) => accumulator * (number - degree * index));
        }
    }
}