Explicit Somos 4 conjecture for the five-parameter generalized Catalan sequence

Let $a_n(p,q,r,s,t)$ be the five-parameter generalized Catalan sequence and let $h_n$ denote the Hankel transform of $\frac{1}{p}a_{n+1}(p,q,r,s,t)$. A $(\alpha,\beta)$ Somos $4$ sequence satisfies

$$e_n=\frac{\alpha e_{n-1}e_{n-3}+\beta e_{n-2}^2}{e_{n-4}}.$$

Five-parameter explicit Somos 4 conjecture. The Hankel transform is a $((pt)^2,-t^2(p^2s+pqr-q^2))$ Somos $4$ sequence. This gives the parameters predicted by the preceding universal conjecture.