Donald Knuth’s 20th Annual Christmas Tree Lecture: (3/2)-ary Trees

In previous lectures Professor Knuth has discussed binary trees, ternary trees, quaternary trees, etc., which are enumerated by the coefficients of important functions called generalized binomial series of order 2, 3, 4, etc. What happens when we consider generalized binomial series of order 3/2, or of other fractional orders? The answer is pretty amazing.