Zeros Conjecture for the $2$-factors of $A(n)$ and $Q(n)$

For an integer $x$ and prime $p$, let $[x]_p$ denote the largest power of $p$ dividing $x$, with $[0]_p=\infty$. Let $A(n)$ be the factorial-numerator sequence from the Taylor partial sums of $e$, and let $Q(n)$ be the denominator sequence of the continued-fraction convergents of $e$. Zeros Conjecture. For each $n\geq 0$,

$$[Q(3n)]_2\leq 4[n(n+2)]_2,$$ $$[Q(3n+1)]_2\leq 2[n+1]_2,$$ $$[Q(3n+2)]_2=1,$$

and

$$[A(n)]_2\leq (n+1)^2.$$

These bounds locate the zeros modulo powers of $2$ and are used in the paper's conditional proof of the partial-sum conjecture. The conjecture is presented as supported by tables and remains unverified in the supplied text.