Descendants in heap ordered trees or a triumph of computer algebra

A heap ordered tree with n nodes (“size n”) is a planted plane tree together with a bijection from the nodes to the set {1, . . . , n} which is monotonically increasing when going from the root to the leaves. We consider the number of descendants of the node j in a (random) heap ordered tree of size n ≥ j. Precise expressions are derived for the probability distribution and all (factorial) moments. AMS Subject Classification. 05A15 (primary) 05C05 (secondary) 1. Heap ordered trees A heap ordered tree with n nodes (“size n”) might be described as a planted plane tree together with a bijection from the nodes to the set {1, . . . , n} which is monotonically increasing when going from the root to the leaves.