nested combination

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

Vertical reversal of duplicate combinations

$ H^n_k = \binom{n + k - 1}{k} = \binom{n + k - 1}{n - 1} = H^k_{n-1}

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