Hoffman's coefficient formula conjecture for Louchard's asymptotic series

Let $I_n$ denote the coefficients in Louchard's asymptotic expansion of the integral in the paper. There is a sequence $a_0,a_1,a_2,\ldots$ of rational numbers beginning with $-2,1,-2,\frac{17}{2},-62,\ldots$ such that, for $n\geq 2$,

$$I_n=\frac18\sum_{j=2}^n(-1)^n a_{\lfloor\frac{j-1}{2}\rfloor}\zeta(\bar j,\{1\}_{n-j}).$$

Hoffman's coefficient formula conjecture. This sequence gives every coefficient $I_n$ in terms of alternating multiple zeta values. The formula is motivated by the explicitly computed cases, but no general proof is supplied.