Binomial coefficients are the numeric factors of the products in a power of a binomial such as (x + y)n. For example, (x + y)2 = x2 + 2 x y + y2 has the coefficients 1 2 1. Binomial coefficients can be calculated using Pascal''s triangle:
1 n = 0
1 1
1 2 1
1 3 3 1
1 4 6 4 1 n = 4
Each new level of the triangle has 1''s on the ends; the interior numbers are the sums of the two numbers above them. Write a program that includes a recursive function to produce a list of binomial coefficients for the power n using the Pascal''s triangle technique. For example,
Input = 2 Output = 1 2 1
Input = 4 Output = 1 4 6 4 1