Guys, I'm trying to prove that [math]\sum ^{n}_{k=1}k\binom{n}{k}^2= n\binom{2n-1}{n-1}[/math]And at the n+1th step I'm doing this [math]\sum ^{n+1}_{k=1}k\binom{n}{k}^2=\sum ^{n}_{k=1}k\binom{n}{k}^2+ k\binom{n}{k}^2[/math] and then I'm using the inductive hypothesis and I'm getting:[math]n\binom{2n-1}{n-1}+[/math] and I'm stuck right here I don't know how to write [imath]k\binom{n}{k}^2[/imath], can someone tell me what am I doing wrong.