The coefficient of  $x^p$ in the expansion of ${(x^2+\frac{1}{x})}^{2n}$ is

${(x^2+\frac{1}{x})}^{2n}$

$r=\frac{np-k}{p+q}$

$n=2n,p=2,q=1,k=p$

$r=\frac{4n-p}{3}$

$T_{r+1}{=}^{2n}{C}_{\frac{4n-p}{3}}{\left(x^2\right)}^{2n-\frac{4n-p}{3}}{\left(\frac{1}{x}\right)}^{\frac{4n-p}{3}}$

${=}^{2n}{C}_{\frac{4n-p}{3}}{\left(x^2\right)}^{\frac{6n-4n+p}{3}}{\left(\frac{1}{x}\right)}^{\frac{4n-p}{3}}$

${=}^{2n}{C}_{\frac{4n-p}{3}}{x}^{\frac{4n+2p}{3}}{x}^{\frac{-4n+p}{3}}$

${ }^{2n}{C}_{\frac{4n-p}{3}}.x^p$

$=\frac{2n!}{(2n-\frac{(4n-p)}{3}!)\frac{(4n-p)}{3}!}$

$\frac{2n!}{\frac{(2n+p)!}{3}\frac{(4n-p)!}{3}}$

$\frac{\left(2n\right)!}{\left(\frac{4n-p}{3}\right)!.\left(\frac{2n+p}{3}\right)!}$