|Journal of Integer Sequences, Vol. 8 (2005), Article 05.1.8|
Abstract: Nicholas Pippenger and Kristin Schleich have recently given a combinatorial interpretation for the second-order super-Catalan numbers : they count "aligned cubic trees" on interior vertices. Here we give a combinatorial interpretation of the recurrence it counts these trees by number of deep interior vertices where "deep interior" means "neither a leaf nor adjacent to a leaf".
(Concerned with sequences
Received February 1 2005; revised version received March 2 2005. Published in Journal of Integer Sequences March 2 2005.