A sapphire high-pressure NMR cell, capable of independently controlling sample pressure, temperature, and concentration, is used to measure C-13 spin-lattice relaxation times for carbons 1, 5, and 9 of l-decanol in dense carbon dioxide at pressure between 80 and 200 atm. These NMR experiments, carried out along four isotherms between 288 and 348 K, provide relaxation data for l-decanol in liquid and supercritical fluid CO2. The nuclear spin-lattice relaxation mechanisms for carbons 1, 5, and 9 of l-decanol as well as for the carbon nucleus in carbon dioxide of this mixture are discussed. The relaxation data are analyzed using a modified Stokes-Einstein-Debye equation, together with an AK model, that postulates the formation of CO2 clusters with the l-decanol molecule in CO2-decanol mixture at supercritical and near-critical liquid densities. Such CO2 cluster formation with methanol molecules was also detected in earlier relaxation measurements in CO2-methanol mixtures at the comparable densities. Possible solvent clustering gradients along the aliphatic chain in l-decanol in dense CO2 are also suggested.