Irreducibility conjecture for reciprocal subsum numerators

Let $n\geq 1$, and let $\mathrm{num}(n,x)$ denote the numerator polynomial associated with sums of reciprocals of subsum polynomials over partitions of $n$. Irreducibility conjecture. For every $n\geq 1$, the polynomial $\mathrm{num}(n,x)$ is irreducible over the integers. This is supported by numerical evidence and is posed as an open question.