Too much Binomial!

Algebra Level 4

\[ (C_0 + C_1)(C_1 + C_2)(C_2 + C_3)\cdot \cdot \cdot (C_{n-1} + C_n)\]

Let \(C_k\) denote the binomial coefficient \( \dbinom {n}{k} \), can you simplify the product above for positive integer \(n > 1 \)?

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