\displaystyle \sum_{l=0}^{n}{ 2n+1 \choose l}=\sum_{l=0}^{n}{ 2n+1 \choose 2n+1-l}=\sum_{l=0}^{n}{ 2n+1 \choose n+1+l }=\sum_{l=n+1}^{2n+1}{ 2n+1 \choose l }