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Following the ideas of Rosenbloom [7] and Hayman [5], Luis B\'aez-Duartegives in [1] a probabilistic proof of Hardy-Ramanujan's asymptotic formula forthe partitions of an integer. The main principle of the method relies on theconvergence in law of a family of random variables to a gaussian variable. Inour work we prove a theorem of the Liapounov type (Chung [2]) that justifiesthis convergence. To obtain simple asymptotic formul{\ae} a condition of theso-called strong Gaussian type defined by Luis B\'aez-Duarte is required; wedemonstrate this in a situation that make it possible to obtain a classicalasymptotic formula for the partitions of an integer with distinct parts(Erd\"os-Lehner [4], Ingham [6]).

Une \'etude asymptotique probabiliste des coefficients d'une s\'erie enti\`ere