Ab initio electronic structure calculations on Snn (n≤20) clusters using ultrasoft pseudopotentials and generalized gradient approximation for the exchange-correlation energy show the binding energies of clusters with n≥10 to be only about 11% less than the calculated bulk value. This is likely to be responsible for the recently reported [Phys. Rev. Lett. 85, 2530 (2000)] higher melting temperatures of these clusters than the bulk value. The growth behavior is found to differ from the one known for Si and Ge clusters at n≥8 but 10- and 18- to 20-atom clusters are similar. The calculated lowest energy fragmentation products are in excellent agreement with experiments and suggest that the lowest energy structures, obtained here, are close to the global minima.