Let Formula: see text denote the number of partitions of Formula: see text into distinct odd parts. In this paper, we prove that the quartic Jensen polynomial associated with Formula: see text: Formula: see text has four distinct real roots for all Formula: see text. To achieve this, we establish several inequalities for Formula: see text by utilizing its arbitrary-precision error estimates. Furthermore, we confirm the positivity of a class of third-order determinants with entries given by Formula: see text, which can be viewed as a generalization of previous results on third-order Toeplitz matrices related to Formula: see text.
Deng et al. (Fri,) studied this question.