Odd-positive coefficient conjecture for the rational-surface polynomials $B_{4n}$

Let $h$ and $p$ be the generators used in the paper for the polynomial expressions $B_{4n}$. For every integer $n$, there is a nonnegative integer $l(n)$ such that $B_{4n}/2^{l(n)}$ is a polynomial in $h$ and $p$. Odd-positive coefficient conjecture. For every $n$, all coefficients of this polynomial are odd positive integers. The conjecture is motivated by the explicit computations of $B_{4n}$ and is supported by the previously computed cases, but no resolution is supplied here.