We investigate a large class of symmetric orthogonal polynomial sequences \((R_n)_{n\in {\mathbb {N}}_0}\) , which are normalized by \(R_n(1)=1\) for all \(n\in {\mathbb {N}}_0\) . Especially we are focussing on sequences with non-negative linearization coefficients, i.e., fulfilling property (P). By switching the coefficients within the three-term recurrence relation of \((R_n)_{n\in {\mathbb {N}}_0}\) one gets a related orthogonal polynomial sequence \((Q_n)_{n\in {\mathbb {N}}_0}\) . In particular, the case when both \((R_n)_{n\in {\mathbb {N}}_0}\) and \((Q_n)_{n\in {\mathbb {N}}_0}\) have positive linearization coefficients is investigated. We examine the power-associated ultraspherical polynomials.
