How to print the Pascal's extended triangle for negative numbers?

Question

(https://i.stack.imgur.com/v9sj1.png)

Hi all, I am currently trying to calculate and print out the pascals extended triangle for negative numbers (-1, -2, ..., -10)

I am aware of the math library but I want to try without the usage of libraries, recursion, lists, string and the other related operations.

the ideal output should be something like this:

(https://i.stack.imgur.com/fnmpL.png)

So I have went ahead and coded up my own factorial function, and a attempt at coding the nCk function:

def factorial(n):
    result = 1
    for i in range(1, n+1):
        result = i
    return result

def n_choose_k(n, k):
    return factorial(n) / (factorial(k) * factorial(n-k))

when I tried to validate if it works or not, I picked out a value from the sample output from above, where k equals to 6 and n equals to -7

def factorial(n):
    result = 1
    for i in range(1, n+1):
        result = i
    return result

def n_choose_k(n, k):
    return factorial(n) / (factorial(k) * factorial(n-k))

print(n_choose_k(-7, 6))

^^ what I ran in my program.

the result should be 924 but instead I got 0.166.

Am I calling the functions wrong? Is there an error in my code?

I am a super noob in terms of programming, much feedback is appreciated.

*sidenote im not sure why my images arent showing, also a noob for this website!