We report the first measurements of the kurtosis (kappa), skewness (S) and variance (sigma^2) of net-proton multiplicity (N_p - N_pbar) distributions at midrapidity for Au+Au collisions at sqrt(s_NN) = 19.6, 62.4, and 200 GeV corresponding to baryon chemical potentials (mu_B) between 200 - 20 MeV. Our measurements of the products kappa sigma^2 and S sigma, which can be related to theoretical calculations sensitive to baryon number susceptibilities and long range correlations, are constant as functions of collision centrality. We compare these products with results from lattice QCD and various models without a critical point and study the sqrt(s_NN) dependence of kappa sigma^2. From the measurements at the three beam energies, we find no evidence for a critical point in the QCD phase diagram for mu_B below 200 MeV.
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