Lupu's conjectural formula for $T(a,b)$

Let $a,b\in\mathbb{Z}_{\geq 0}$, and define

$$T(a,b):=t(\{2\}^a,3,\{2\}^b),$$

where $t(s_1,\ldots,s_r)$ is the multiple $t$-value over positive odd integers. Lupu's conjecture for $T(a,b)$. For nonnegative integers $a$ and $b$, one has

$$T(a,b)=\frac{-2}{(2a+1)!}\left(\frac{\pi}{2}\right)^{2a+2b+2}\sum_{n=0}^{\infty}\frac{\zeta(2n)}{(2n+2a+1)(2n+2a+2)\cdots(2n+2a+2b+2)2^{2n}}.$$

This is the second conjectural generalization proposed for the case $b>0$, following known special formulas when $b=0$. The supplied text gives no resolution status.