J. Blieberger, P. Kirschenhofer:

"Generalized Catalan Sequences Originating from the Analysis of Special Data Structures";

Bulletin of the Institute of Combinatorics and its Applications,71(2014), 103 - 116.

Reinterpreting known results on Carlitz's q-Catalan numbers $c_n(q)$ we find a connection between the number of acyclic DJ graphs and these q-analogs. A similar recurrence relation is setup for the number of reducible DJ graphs, a well-known data structure in computer science, this time leading to a different q-analog $C_n(q)$ of Catalan numbers. Using arguments from enumerative combinatorics we establish a complete asymptotic expansion of the numbers $C_n(q)$.

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