Coefficient of x to the p

If $x^p$ occurs in the expansion of ${\left(x^2+\frac{1}{x}\right)}^{2n}$, prove that its coefficient is $\frac{(2n)!}{\left(\frac{4n-p}{3}\right)!\left(\frac{2n+p}{3}\right)!}$.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIII. Binomial Theorem: Positive Integral Index, Examples XIII.a, No. 35