The recent Mw = 9.3 Sumatra-Andaman earthquake on December 26th 2004 has strongly excited the low-frequency seismic modes of the Earth. In particular the large amplitude of the fundamental radial mode 0S0, which consists of a roughly uniform compression and dilatation of the whole Earth, and of the seismic core modes, like 3S2, means that much energy was radiated toward the core. Also the degree one mode 2S1, which corresponds to a translation of the core in the mantle, was clearly observed for the first time without any stacking process on seismometers and on gravimeters. 2S1 is the first harmonic of the degree one mode 1S1, the so-called Slichter triplet. In fact, the Slichter mode is not an elastic spheroidal mode like 2S1 since its main feedback force is the Archimedean force. The Slichter mode corresponds to a translation of the solid inner core inside the fluid outer core. The theory concerning this mode is still poorly constrained and no convincing detection has been suggested yet. This paper presents theoretical predictions of the amplitude of the Slichter mode after the 2004 Sumatra-Andaman earthquake as well as after some largest events in the past decades. The computation is based on the usual normal mode theory for a spherically symmetric non-rotating Earth model. The source parameters are finally investigated to find the optimal seismic mechanism to excite the translational motion of the inner core.