The cyclotomic divisibility conjecture for odd tree powers

Let $\lambda=(\lambda_1,\ldots,\lambda_m)$ be a partition, let $T_\lambda$ be the rooted tree with $n+1$ vertices defined by

$$T_\lambda=\textsc{B}_{+}(\mathtt{Lnr}_{\lambda_1},\ldots,\mathtt{Lnr}_{\lambda_m}),$$

let $k\geq 3$ be an odd integer, and let $\Phi_d$ denote the $d$th cyclotomic polynomial. The cyclotomic divisibility conjecture. The coefficient $\Omega_{q,\textsc{B}_{+}(T_\lambda^k)}$ is divisible by $\Phi_{1+\max\lambda}$.

This conjecture concerns cyclotomic factors in coefficients of the series $\Omega_q$ associated with trees constructed from partitions. The source gives no evidence of a resolution.