If ${\mathrm{S}}_{\mathrm{n}}={\left({ }^{\mathrm{n}}{\mathrm{C}}_0\right)}^2+{\left({ }^{\mathrm{n}}{\mathrm{C}}_1\right)}^2+{\left({ }^{\mathrm{n}}{\mathrm{C}}_3\right)}^2+\dots +{\left({ }^{\mathrm{n}}{\mathrm{C}}_{\mathrm{n}}\right)}^2$, then maximum value of $\left[\frac{{\mathrm{S}}_{\mathrm{n}+1}}{{\mathrm{S}}_{\mathrm{n}}}\right]$ is _________.

(where [.] denotes the greatest integer function)