\[U_{n}\left(x\right)=\sum_{\ell=0}^{\left\lfloor n/2\right\rfloor}\frac{(-1)^{%
\ell}(n-\ell)!}{\ell!\;(n-2\ell)!}(2x)^{n-2\ell}=\left(2x\right)^{n}{{}_{2}F_{%
1}}\left({-\tfrac{1}{2}n,-\tfrac{1}{2}n+\tfrac{1}{2}\atop-n};\frac{1}{x^{2}}%
\right),\]