Let $B_n$ be the $n$-th Catalan Number. We have $ B(x) = \sum_{n \ge 0} B_n x^n = \frac{1-\sqrt{1-4x}}{2x}$.
Does anyone know a closed form of the generating function of the shifted Catalan Numbers, i.e. for chosen $p_0$, for $B_{p_0}(x) = \sum_{n \ge 0} B_{n+p_0} x^n$?