Topological representation zeta function of infinitesimal Heisenberg groups

Let $\mathbb{Q}[\varepsilon_n]=\mathbb{Q}[x]/(x^n)$, and let $\mathbf{H}[\varepsilon_n]$ denote the group scheme obtained from the Heisenberg Lie algebra tensored with $\mathbb{Q}[\varepsilon_n]$. Write $\zeta_{\mathbf{H}[\varepsilon_n],\mathrm{top}}(s)$ for its topological representation zeta function. Topological Heisenberg zeta-function conjecture. One has

$$\zeta_{\mathbf{H}[\varepsilon_n],\mathrm{top}}(s)=\prod_{i=1}^n\frac{is-2i+2}{is-2i+1}.$$

The formula matches the computations for $n=2$ and $n=3$ and is suggested by the conjectured $p$-adic formula; general $n$ remains open.