import numpy as np

def simplex_number_numpy_optimized(d, n):
    # 初始化动态规划表
    dp = np.zeros((d + 1, n + 1), dtype=int)
    dp[1, :] = np.arange(n + 1)  # 初始化一维简单形数
    
    # 递归关系：直接利用 Numpy 数组操作
    for dim in range(2, d + 1):
        dp[dim, 1:] = np.cumsum(dp[dim - 1, 1:])
    
    return dp[d, n]

# 示例：计算 5 维的第 4 项
result = simplex_number_numpy_optimized(20, 9)
print(f"5D 第 4 项：{result}")