First observation of Bs -> D_{s2}^{*+} X mu nu decays

Using data collected with the LHCb detector in proton-proton collisions at a centre-of-mass energy of 7 TeV, the semileptonic decays Bs -> Ds+ X mu nu and Bs -> D0 K+ X mu nu are detected. Two structures are observed in the D0 K+ mass spectrum at masses consistent with the known D^+_{s1}(2536) and $D^{*+}_{s2}(2573) mesons. The measured branching fractions relative to the total Bs semileptonic rate are B(Bs -> D_{s2}^{*+} X mu nu)/B(Bs -> X mu nu)= (3.3\pm 1.0\pm 0.4)%, and B(Bs -> D_{s1}^+ X munu)/B(Bs -> X mu nu)= (5.4\pm 1.2\pm 0.5)%, where the first uncertainty is statistical and the second is systematic. This is the first observation of the D_{s2}^{*+} state in Bs decays; we also measure its mass and width.