# Combinatorial Number Theory!

$\large{4^s \sum_{k=0}^{n-s} { 2s+2k-1 \choose 2s-1} \equiv \alpha \pmod p}$

Let $$p=2n+1$$ be a prime, where $$n$$ is an integer, and let $$s$$ be any integer such that $$1 \leq s \leq n$$. If the above modular equation satisfies, where $$\alpha$$ is a positive integer less than $$p$$, find the value of $$\alpha$$.

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