Question: Prove the double factorial identities: [(2 n)!!=2^{n} n!] and [(2 n-1)!!=frac{(2 n)!}{2^{n} n!}]

Prove the double factorial identities:

\[(2 n)!!=2^{n} n!\]

and

\[(2 n-1)!!=\frac{(2 n)!}{2^{n} n!}\]

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