2338. Count the Number of Ideal Arrays

class Solution:
    def idealArrays(self, n: int, maxValue: int) -> int:
        c = [[0] * 16 for _ in range(n)]
        mod = 10**9 + 7
        for i in range(n):
            for j in range(min(16, i + 1)):
                c[i][j] = 1 if j == 0 else (c[i - 1][j] + c[i - 1][j - 1]) % mod
        dp = [[0] * 16 for _ in range(maxValue + 1)]
        for i in range(1, maxValue + 1):
            dp[i][1] = 1
        for j in range(1, 15):
            for i in range(1, maxValue + 1):
                k = 2
                while k * i <= maxValue:
                    dp[k * i][j + 1] = (dp[k * i][j + 1] + dp[i][j]) % mod
                    k += 1
        res = 0
        for i in range(1, maxValue + 1):
            for j in range(1, 16):
                res = (res + dp[i][j] * c[-1][j - 1]) % mod
        return res