User talk:PaoloMartini

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p(x) = \sum_{i=0}^n a_i x^i
(x - 1)^n = \sum_{i=0}^n {n \choose i } x^{n-i} (-1)^i
{n \choose k} = {n \choose n-k}
(x - 1)^n = \sum_{i=0}^n {n \choose i} x^i (-1)^i
p(x-1) = \sum_{i=0}^n a_i (x - 1)^i
= \sum_{i=0}^n (a_i \sum_{k=0}^n {n \choose k} x^k (-1)^k).