The optimal s-step second order explicit SSP linear multistep method has SSP coefficient $\frac{s-1}{s}$ and Shu-Osher form $$ \begin{align*} \alpha_1 = & \frac{(s-1)^2-1}{(s-1)^2}, & \alpha_s = & \frac{1}{(s-1)^s}, & \beta_1 = & \frac{s}{s-1} \end{align*} $$