Finding Sylvester sequence code

Question

I've written this code to calculate the Sylvester sequence, which is defined as $$s_n = s_{n-1}(s_{n-1}-1)+1$$ where \$s_0=2\$.

def sylvester_term(n):
    """ Returns the maximum number of we will consider in a wps of dimension n

    >>> sylvester_term(2)
    7
    >>> sylvester_term(3)
    43
    """
    if n == 0:
        s_n = 2
        return s_n

    s_n = sylvester_term(n-1)*(sylvester_term(n-1)-1)+1

    return s_n  
    print(s_n)

print(sylvester_term(3))

Answer 1

The print() call at the end of the function is unreachable and should be removed.

There's no need to assign s_n before returning.

PEP 8, the official Python style guide, recommends a space before and after every binary operator.

def sylvester_term(n):
    """docstring here"""
    if n == 0:
        return 2
    else:
        return sylvester_term(n - 1) * (sylvester_term(n - 1) - 1) + 1

Next, you should notice that sylvester_term(n - 1) is used twice in the expression. You should definitely assign that result to a variable, otherwise your function will require drastically more time — O(2ⁿ) instead of O(n).

def sylvester_term(n):
    """Return the maximum number of we will consider in a wps of dimension n

    >>> sylvester_term(2)
    7
    >>> sylvester_term(3)
    43
    """
    if n == 0:
        return 2
    else:
        prev_sylvester_term = sylvester_term(n - 1)
        return prev_sylvester_term * (prev_sylvester_term - 1) + 1