A combinatorial interpretation for a super-Catalan recurrence

Details A combinatorial interpretation for a super-Catalan recurrence A combinatorial interpretation for a super-Catalan recurrence

2004-08-09

arxiv.org/abs/math/0408117v1

Mathematics

Combinatorics

8 pages, LaTeX

Scientific paper

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".

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