Diamond lift of Hirose--Sato's formula involving the Hoffman basis

In this paper, we give a new proof of Hirose–Sato’s formula for the expansion of $\zeta (\{2{\}}^{a_1-1},3,\dots ,\{2{\}}^{a_r-1},3,\{2{\}}^{c-1},1,\{2{\}}^{b_1},\dots ,1,\{2{\}}^{b_s})$ in the Hoffman basis, using the drop 1 relation.