function to calculate coin change recursively using dynamic programming

coin_change.py

n = 10
c = [2, 3, 5, 6]

ways = [[0 if i < min(c) else - 1 for i in range(n + 1)] for j in c]

def num_ways(n, c):
    row = len(c) - 1
    # base case
    if n < min(c): return 0
    
    # if not pre calculated
    if ways[row][n] == -1:
        if n in c: ways[row][n] = 1
        else: ways[row][n] = 0

        for i in range(len(c)):
            ways[row][n] += num_ways(n - c[i], c[i:])

    return ways[row][n]

num_ways(n+1, c)

print(ways[len(c)-1][n])