Prospects for multiband gravitational-wave astronomy after GW150914

We show that the black hole binary (BHB) coalescence rates inferred from the advanced LIGO (aLIGO) detection of GW150914 imply an unexpectedly loud GW sky at milli-Hz frequencies accessible to the evolving Laser Interferometer Space Antenna (eLISA), with several outstanding consequences. First, up to thousands of BHB will be individually resolvable by eLISA; second, millions of non resolvable BHBs will build a confusion noise detectable with signal-to-noise ratio of few to hundreds; third -- and perhaps most importantly -- up to hundreds of BHBs individually resolvable by eLISA will coalesce in the aLIGO band within ten years. eLISA observations will tell aLIGO and all electromagnetic probes weeks in advance when and where these BHB coalescences are going to occur, with uncertainties of