An odd 3-strand pretzel knot $K=P(p,q,r)$ has $\Delta_K(t)=1$ if $pq+pr+qr=1$. This fact, along with a theorem of Fintushel and Stern (every odd 3-pretzel knot with trivial Alexander polynomial is not smoothly slice) generates an infinite amount of topologically slice knots that are not smoothly slice. I am trying to look at the same thing for an arbitrary $n$-stranded odd Pretzel knot. Does there exist a general formula, such that an odd Pretzel knot $K=P(p_1,p_2,…p_n)$ has $\Delta_K(t)=1$ if some relation on $p_1,…,p_n$ is satisfied?
Edit: Is there any information on what that relation is? I am curious to see if it remains homogeneous as $n$ increases.