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China Mathematical Olympiad 1994 problem5

Source: China Mathematical Olympiad 1994 problem5

September 17, 2013
algebra unsolvedalgebrapolynomialInteger Part

Problem Statement

For arbitrary natural number nn, prove that ∑k=0nCnk2kCn−k[(n−k)/2]=C2n+1n\sum^n_{k=0}C^k_n2^kC^{[(n-k)/2]}_{n-k}=C^n_{2n+1}, where C00=1C^0_0=1 and [n−k2][\dfrac{n-k}{2}] denotes the integer part of n−k2\dfrac{n-k}{2}.
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