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I want to rewrite the series $$1 + a + a(a-1) + a(a-1) (a-2) +\cdots+a(a-1)\cdots(a-(n-1))$$ as $(a^n-1)Y$ or $(a^{n-1}-1)Y$

Short-form: $$\{1+\sum_{i=1}^{n} \prod_{j=0}^{i-1}(a-j)\}$$ as $(a^n-1)Y$ or $(a^{n-1}-1)Y$

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2 Answers 2