Recursive definition of products

Question

Let $(M,*)$ be a Magma. How can one recursively define products such as $(a_1*a_2)*(a_3*(a_4*a_5))$ and so on ? The basic idea is i think that we have something like : $P^1(a_1)=a_1$ and $P^n(a_1,....,a_n)=P^k(a_1,..a_k)*P^l(a_{k+1},..,a_n)$, with $k+l=n$. Any help is appreciated.