在参考Mathematica Integer partition of n into k parts recurrence中的线程后，提出了以下解决方案：

def p(n: int, k: int) -> int:
   memo: list[list[int]] = [[0 for _ in range(k+1)] for _ in range(n + 1)]
   for i in range(1,n + 1):
       memo[i][1] = 1

   for i in range(2,n + 1):
       for j in range(2, k+1):
           memo[i][j] += memo[i-1][j - 1]
           if i - j >= j :
               memo[i][j] += memo[i - j][j]

   return memo[n][k]

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