I have been able to prove the following using the snake oil method:
$$\sum_{k \ge 0} C_k {{n-2k} \choose {l-k}} = {{n+1} \choose {l}}$$ where $l,n$ are positive integers and $C_k$ is the $k$-th Catalan number.
Question: Can someone please show me the combinatorial proof for the case $l \le n$? Thanks