Question 112
Prove for any positive integer $n$:
$$
\sum_{k=0}^{n-1} \frac{\left(\binom{n-1}{k}\right)^2}{k+1} = \frac{\binom{2n}{n}}{2n}
$$
$$
\sum_{k=0}^{n-1} \frac{\left(\binom{n-1}{k}\right)^2}{k+1} = \frac{\binom{2n}{n}}{2n}
$$
MathNet 2009-part-04 — 175 problems (EN–VI) Question 112
Math Olympiad Vault · MathNet 2009-part-04 — 175 problems (EN–VI)