Specialized 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. Assume

$$r=1,\qquad t=1,\qquad s=q-p+1.$$

Specialized generalized Catalan Somos 4 conjecture. The Hankel transform of $a_n(p,q,1,q-p+1,1)$ is a $(p^2,p^3-pq+q^2-p^2(1+q))$ Somos $4$ sequence. This is the second conjecture in the five-parameter discussion and concerns the indicated parameter specialization.