The 2-adic valuation of plane partitions and totally symmetric   partitions
  This paper confirms a conjecture of Amdeberhan and Moll that the power of 2 dividing the number of plane partitions in an n-cube is greater than the power of 2 dividing the number of totally symmetric plane partitions in the same cube when n is even, and less when n is odd. 
William J. Keith
math.CO