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$$ nLn(x) = (2n - 1)xL{n-1}(x) - (n - 1)L_{n-2}(x) $$

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$$ nLn(0) = - (n - 1)L{n-2}(0) $$

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$$ Ln(0) = -\frac{n - 1}{n} L{n-2}(0) $$

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• $L2(0) = -\frac{2 - 1}{2} L0(0) = -\frac{1}{2} \times 1 = -\frac{1}{2}$
• $L3(0) = -\frac{3 - 1}{3} L1(0) = -\frac{2}{3} \times 0 = 0$
• $\vdots$

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