I am embarrassed to admit that though I love this tree every time I visit the Japanese Garden at the Denver Botanic Garden, I still have not confirmed what kind of tree it is!  I have an affinity for  its gnarly branches, even when the red fruit is gone for the season.  I have photographed it many many times.  It sits just inside the gate to the Tea House.  I have only found that gate open one time, allowing me to photograph the tree from the other side.  Surely that will appear on my website eventually too!