負の二項定理と重複組合せ

• $(1-x{)}^{-d}={\sum }_{n=0}^{\infty }{H}_{d-1}^{n+1}{x}^n$

負の二項定理:

• $(1-x{)}^{-d}={\sum }_{n=0}^{\infty }(\genfrac{}{}{0ex}{}{n+d-1}{d-1})x^n$ 重複組合せ:
• $H_k^n=\left(\genfrac{}{}{0ex}{}{n+k-1}{k}\right)=\frac{(n+k-1)!}{k!(n-1)!}$