I going over a chapter in my book for discrete mathematics and there is the following rewrite of a summation. They present
$$\ell_{n}=\sum_{i=0}^{n / 2-1} \ell_{2 i} \ell_{n-2 i-2} $$ and state that it is valid in this case for even values of n≥2. Then they say that we can simplify it by rewriting it as
$$ \begin{array}{c}{\ell_{n}=\sum_{k \geq 0} \ell_{k} \ell_{n-k-2}} \\ {\ell_{n}=\sum_{k \geq 0} \ell_{k} \ell_{n-k-2}+[n=0]}\end{array} $$ And i just dont quite understand how they do this?