Want to print each iteration of factorial program

[perfringo]

I observe following problematic areas:
- base case is not printed out (one can't understand if whole 'process' is not printed out)
- this function is not defensive against negative values (RecursionError)

For better understanding one can write (requires 3.6 <= Python due to f-strings):

def _factorial_sample_(n): 
    if n < 0: 
        raise ValueError('No factorials for negative numbers') 
    if n == 0 or n == 1: 
        print(f'n is {n}, carrying over {1}, this is base case') 
        return 1 
    else: 
        result = n * _factorial_sample_(n-1) 
        print(f'n is {n}, carrying over {result}') 
        return result

With different arguments one will get:

>>> _factorial_sample_(5)                                                                                     
n is 1, carrying over 1, this is base case
n is 2, carrying over 2
n is 3, carrying over 6
n is 4, carrying over 24
n is 5, carrying over 120
120
>>> _factorial_sample_(0)
n is 0, carrying over 1, this is base case
1
>>> _factorial_sample_(1)                                                                                     
n is 1, carrying over 1, this is base case
1
>>> _factorial_sample_(-5)
/.../
ValueError: No factorials for negative numbers

To your original problem: you probably should use memoization