Nicholas Pippenger and Kristin Schleich have recently given a combinatorial interpretation for the second-order super-Catalan numbers (u_{n})_{n≥0} = (3, 2, 3, 6, 14, 36, ...): they count “aligned cubic trees” on n interior vertices. Here we give a combinatorial interpretation of the recurrence u_{n} = ∑_{k=0}^{n/2−1} \binom{n−2}{2k}2^{n−2−2k}u_{k} : it counts these trees by number of deep interior vertices where “deep interior” means “neither a leaf nor adjacent to a leaf”.