  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
internal vertices. Here we give a combinatorial interpretation of the
recurrence u_{n} = Sum_{k=0}^{n/2-1} ({n-2}choose{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".
