Lupu's conjectural formula for $H(a,b)$

Let $a,b\in\mathbb{Z}_{\geq 0}$, and let $H(a,b)$ denote the quantity used in Lupu's Zagier-type formula for multiple $t$-values. Lupu's conjecture for $H(a,b)$. For nonnegative integers $a$ and $b$, one has

$$H(a,b)=\frac{-4\pi^{2a+2b+2}}{(2a+2)!}\sum_{n=0}^{\infty}\frac{\zeta(2n)}{(2n+2a+2)(2n+2a+3)\cdots(2n+2a+2b+3)2^{2n}}.$$

This is one of two conjectural extensions, for the general case $b>0$, of formulas previously established for $b=0$. The supplied text gives no resolution status.