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Solution

$\text{Coeff}{x^n},(1+x)^{2n}=\binom{2n}{n}$ and $\text{Coeff}{x^n},(1+x)^{2n-1}=\binom{2n-1}{n}$. $\displaystyle \binom{2n}{n}=\frac{(2n)}{n,n}=\frac{2n}{n}\cdot\frac{(2n-1)}{n,(n-1)}=2\binom{2n-1}{n}$. So ratio $=2:1$.