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

$ (1-x)^{-d} = \sum_{n=0}^\infty \binom{n+d-1}{d-1}x^n

$ H^n_k = \binom{n + k - 1}{k} = \frac{(n + k - 1)!}{k!(n - 1)!}