常用组合数计算公式

版权声明：欢迎转载，不要求署名~~~ https://blog.csdn.net/shadandeajian/article/details/82084087

• $C_n^m=C_{n-1}^{m-1}+C_{n-1}^{m}$
  
  

• $m*C_{n}^{m}=n*C_{n-1}^{m-1}$
  
  
• $C_{n}^{0}+C_{n}^{1}+C_{n}^{2}+\dots+C_{n}^{n}=2^n$
  
  
• $1C_{n}^{1}+2C_{n}^{2}+3C_{n}^{3}+\dots+nC_{n}^{n}=n2^{n-1}$
  
  
• $1^2C_{n}^{1}+2^2C_{n}^{2}+3^2C_{n}^{3}+\dots+n^2C_{n}^{n}=n(n+1)2^{n-2}$
  
  
• $\frac{C_{n}^{1}}{1}-\frac{C_{n}^{2}}{2}+\frac{C_{n}^{3}}{3}+\dots+(-1)^{n-1}\frac{C_{n}^{n}}{n}=1+\frac{1}{2}+\frac{1}{3}+\dots+\frac{1}{n}$
  
  
• $(C_{n}^{0})^2+(C_{n}^{1})^2+(C_{n}^{2})^2+\dots+(C_{n}^{n})^2=C_{2n}^{n}$