具体数学-扰动法

from scipy.special import comb

n = int (input("n: "))

k = int (input("k: "))

sum1 = 0

for j in range(0, k):
    for i in range(0, n+1):
       sum1 = sum1 + (i**j)*comb(k+1,j)
       
    
result = ((n+1)**(k+1) - sum1)/comb(k+1,k) 

print(result)

 python 中计算排列组合：

1. 调用scipy计算

>> from scipy.special import comb, perm
>> perm(3, 2)
6.0
>> comb(3, 2)
3.0

2. 调用 itertools 获取排列组合的全部情况数

>> from itertools import combinations, permutations
>> permutations([1, 2, 3], 2)
<itertools.permutations at 0x7febfd880fc0>
                # 可迭代对象
>> list(permutations([1, 2, 3], 2))
[(1, 2), (1, 3), (2, 1), (2, 3), (3, 1), (3, 2)]

>> list(combinations([1, 2, 3], 2))
[(1, 2), (1, 3), (2, 3)]