Ballantine–Beck–Feigon–Maurischat's log-concavity conjecture for partition denominators

Let $\operatorname{den}(n,x)$ be the ordinary denominator of the reciprocal of the partition polynomial for $n$. Ballantine–Beck–Feigon–Maurischat's log-concavity conjecture. The sequence of coefficients of $\operatorname{den}(n,x)$ is log-concave except for $n=3,5,6,7$. This is a coefficient-shape conjecture for ordinary partition denominators; its resolution is not specified in the supplied text.