Using recursion to generate list form of Pascal's Triangle

Khayyam Triangle

# Khayyam Triangle

# The French mathematician, Blaise Pascal, who built a mechanical computer in
# the 17th century, studied a pattern of numbers now commonly known in parts of
# the world as Pascal's Triangle (it was also previously studied by many Indian,
# Chinese, and Persian mathematicians, and is known by different names in other
# parts of the world).

# The pattern is shown below:

#                    1
#                   1 1
#                  1 2 1
#                 1 3 3 1
#                1 4 6 4 1
#                   ...

# Each number is the sum of the number above it to the left and the number above
# it to the right (any missing numbers are counted as 0).

# Define a procedure, triangle(n), that takes a number n as its input, and
# returns a list of the first n rows in the triangle. Each element of the
# returned list should be a list of the numbers at the corresponding row in the
# triangle.
        
def triangle(n):
    if n == 0:
        return []
    if n == 1:
        return [[1]]
    if n > 1 :
        old_triangle = triangle(n-1)
        previous_row = old_triangle[-1]
        middle_nums = []
        for i in range(0,n-2):
            temp = previous_row[i] + previous_row[i+1] 
            middle_nums.append(temp)
        last_row = [1] + middle_nums + [1]
        return old_triangle + [last_row]