{(-1)^{n-k}}(k+1)\frac{L_k}{k!}\frac{L_{k+1}}{(k+1)!}+{(-1)^{n-k}}k\frac{L_k}{k!}\frac{L_{k-1}}{(k-1)!}=(-1)^{n-k}\frac{2k+1-x}{(k!)^{2}}L^{2}_{k}(x)