Computationally Efficient Bounds for the Sum of Catalan Numbers
  Easily computable lower and upper bounds are found for the sum of Catalan numbers. The lower bound is proven to be tighter than the upper bound, which previously was declared to be only an asymptotic. The average of these bounds is proven to be also an upper bound, and empirically it is shown that the average is superior to the previous upper bound by a factor greater than (9/2). 
Kevin Topley
math.CO