Python| sympy.binomial_coefficients() 方法

借助sympy.binomial_coefficients()方法，我们可以找到给定整数的二项式系数。该方法返回一个包含对的字典${(k1, k2) : C_kn}$在哪里$C_kn$是二项式系数和$n=k1+k2$ .

Syntax: binomial_coefficients(n)

Parameter:
n – It denotes an integers.

Returns: Returns a dictionary containing pairs (k1, k2) : C_kⁿ where C_kⁿ are binomial coefficients and n = k1 + k2.

示例 #1：

# import binomial_coefficients() method from sympy
from sympy.ntheory import binomial_coefficients
  
n = 6
  
# Use binomial_coefficients() method 
binomial_coefficients_n = binomial_coefficients(n) 
      
print("binomial_coefficients({}) = {} ".format(n, binomial_coefficients_n))

输出：

binomial_coefficients(6) = {(3, 3): 20, (1, 5): 6, (6, 0): 1, (0, 6): 1, (4, 2): 15, (5, 1): 6, (2, 4): 15}

示例 #2：

# import binomial_coefficients() method from sympy
from sympy.ntheory import binomial_coefficients
  
n = 9
  
# Use binomial_coefficients() method 
binomial_coefficients_n = binomial_coefficients(n) 
      
print("binomial_coefficients({}) = {} ".format(n, binomial_coefficients_n))

输出：

binomial_coefficients(9) = {(2, 7): 36, (9, 0): 1, (8, 1): 9, (5, 4): 126, (6, 3): 84, (4, 5): 126, (1, 8): 9, (3, 6): 84, (0, 9): 1, (7, 2): 36}