Is there a nice closed form for the integral of $(\tan x)^{2n}$?

I just want to know if there is a nice closed form for this integral:

$$\int_{}^{}(\tan x)^{2n}dx$$

I know that a reduction formula exists and this is what I get by following it:

$$\begin{align*}\int\tan^{2n}{x}dx &= \int\tan^{2n-2}{x}\left(\sec^2{x}-1\right)dx\\&= \int\tan^{2n-2}{x} \sec^2{x}dx-\int\tan^{2n-2}{x}dx\\&=\frac{1}{2n-1}\tan^{2n-1}{x}-\int\tan^{2n-2}{x}dx\end{align*}$$

but still I wasn't reaching any answer. I want (if possible) one of those answers where there are binomial coefficients and exponents etc.

In short I just want a closed form for this integral so that I can just plug a value of n and get the answer.