A note on sums of independent random variables
  In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Lata{\l}a on bounds on moments of such sums. We also give a new proof of Lata{\l}a's result for nonnegative random variables, and improve one of the constants in his inequality. 
Pawe{\l} Hitczenko and Stephen Montgomery-Smith