We consider a natural integer $n$ and a complex number $a$. Using Abel's binomial identity
$$\forall (a, x, y) \in \mathbb{C}^3, \quad (x+y)^n = y^n + \sum_{k=1}^{n} \binom{n}{k} x(x - ka)^{k-1}(y + ka)^{n-k},$$
establish the relation
$$\forall (a, y) \in \mathbb{C}^2, \quad ny^{n-1} = \sum_{k=1}^{n} \binom{n}{k} (-ka)^{k-1}(y + ka)^{n-k}.$$