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:

function multiFact (n, degree)
    local fact = 1
    for i = n, 2, -degree do
        fact = fact * i
    end
    return fact
end

print("Degree\t|\tMultifactorials 1 to 10")
print(string.rep("-", 52))
for d = 1, 5 do
    io.write(" " .. d, "\t| ")
    for n = 1, 10 do
        io.write(multiFact(n, d) .. " ")
    end
    print()
end