Separate zero-th degree terms

Question

I have following triple summation expression: $$\sum_{i=0}^{m}\sum_{j=0}^{i}\sum_{k=0}^{n}a_{i,j,k}x^{i-j+k}.$$ I want to separate terms with $0$-th degree of $x$ from others. I understand that $k=0$ as $i-j$ is non-negative. Then,
$$\sum_{i=0}^{m}\sum_{j=0}^{i}a_{i,j,0}x^{i-j}+\sum_{i=0}^{m}\sum_{j=0}^{i}\sum_{k=1}^{n}a_{i,j,k}x^{i-j+k}.$$ I understand that I should consider only the terms with $i=j$ but I am unable to write its in nice mathematical compact form.

Can someone please guide me?

Answer 1

$$\sum_{i=0}^{m}a_{i,i,0}+\sum_{i=0}^{m}\sum_{j=0}^{i-1}a_{i,j,0}x^{i-j}+\sum_{i=0}^{m}\sum_{j=0}^{i}\sum_{k=1}^{n}a_{i,j,k}x^{i-j+k}$$