The denominator conjecture for corolla coefficients

Let $\mathtt{Crl}_n$ denote the corolla with $n$ leaves, let $\sympawn_{\mathtt{Crl}_n}$ be its coefficient, and let $\Phi_d$ denote the $d$th cyclotomic polynomial. The denominator conjecture. The denominator of $\sympawn_{\mathtt{Crl}_n}$ is

$$\prod_{d=2}^{n+1}\Phi_d.$$

This conjecture concerns the regularity of the denominators of coefficients associated with corollas; the surrounding discussion gives examples and notes that the observed denominators appear simple and regular. No resolution is given in the source.