I can show that these two sums are equal by writing out all terms, but is there a quick way to see the equality:

$$\sum\_{i=0}^n\sum\_{j=0}^i a\_jb\_{i-j}c\_{n-i} = \sum\_{i=0}^n\sum\_{j=0}^{n-i} a\_ib\_{j}c\_{n-i-j} $$

(this question popped up while checking that the formal power series over a commutative ring is a commutative ring, in particular, when checking that the multiplicative associativity is satisfied.)