Let \(n \in \mathbb{N}_{> 0}\) and consider the binomial expansion of \[(x+y)^n = \sum\limits_{k=0}^{k=n} \alpha_k x^k y^{n-k}\] where \(\alpha_k \in \mathbb{R}\)

Calculate \(\sum\limits_k \alpha_k\) and express your answer as a function of \(n\).

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