  The decay $B_c^+ \to \psi(2S)\pi^+$ with $\psi(2S) \to \mu^+\mu^-$ is
observed with a significance of $5.2\,\sigma$ using $pp$ collision data
corresponding to an integrated luminosity of $1.0\,\invfb$ collected by the
LHCb experiment. The branching fraction of $B_c^+ \to \psi(2S)\pi^+$ decays
relative to that of the $B_c^+ \to J/\psi\pi^+$ mode is measured to be
\begin{equation*} \frac{\mathcal{B}(B_c^+ \to \psi(2S)\pi^+)}{\mathcal{B}(B_c^+
\to J/\psi\pi^+)} = 0.250 \pm 0.068 \,\text{stat} \pm 0.014 \,\text{\syst} \pm
0.006 \,(\mathcal{B}). \end{equation*} The last term is the uncertainty on the
ratio $\mathcal{B}(\psi(2S) \to \mu^+\mu^-)/\mathcal{B}(J/\psi \to
\mu^+\mu^-)$.
