MHB Relation between Hermite and associated Laguerre

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Please help me in proving the following expression

$$H_{2n}(x)=(-1)^n2^{2n}n!L_n^{-\frac{1}{2}}(x^2)$$

where $$H_n$$ is the Hermite polynomial and $$L_n^{-\frac{1}{2}}$$ is the associated Laguerre polynomial.
 
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