  The decays $ \Lambda_b^0 \to \psi(2S)pK^-$ and $ \Lambda_b^0 \to J/\psi \pi^+
\pi^- pK^-$ are observed in a data sample corresponding to an integrated
luminosity of 3fb$^{-1}$, collected in proton-proton collisions at 7 and 8TeV
centre-of-mass energies by the LHCb detector. The $\psi(2S)$ mesons are
reconstructed through the decay modes $\psi(2S)\to\mu^+\mu^-$ and $\psi(2S)\to
J/\psi\pi^+\pi^-$. The branching fractions relative to that of $ \Lambda_b^0
\to J/\psi pK^-$ are measured to be \begin{eqnarray*}
  \frac{\mathcal{B}(\Lambda_b^0 \to \psi(2S) pK^-)}
  {\mathcal{B}(\Lambda_b^0 \to J/\psi pK^-)}
  & = & (20.70\pm 0.76\pm 0.46\pm 0.37)\times10^{-2} \,,
  \frac{\mathcal{B}(\Lambda_b^0 \to J/\psi \pi^+ \pi^- pK^-)}
  {\mathcal{B}(\Lambda_b^0 \to J/\psi pK^-)}
  & = & (20.86\pm 0.96\pm 1.34)\times10^{-2} \,, \end{eqnarray*} where the
first uncertainties are statistical, the second are systematic and the third is
related to the knowledge of $J/\psi$ and $\psi(2S)$ branching fractions.
  The mass of the $\Lambda_b^0$ baryon is measured to be $$ M(\Lambda_b^0) =
5619.65 \pm 0.17 \pm 0.17\mathrm{MeV}/c^2,$$ where the uncertainties are
statistical and systematic.
