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May 7, 2022 at 11:53 vote accept Svjetlan Feretic
May 7, 2022 at 11:53 comment added Svjetlan Feretic Thank you for the quick and detailed answer. In fact, my two Narayana-enumerated objects are: 1) Dyck paths with $2n$ steps and $k$ rises at even level, and 2) Dyck paths with $2n$ steps and $k-1$ rises at odd level. Now it remains to find a proper reference for those two objects. (In fact, I could also write that those two objects are classical.) In "Elements of the sets enumerated by super-Catalan numbers", the authors cite a 1999 paper by Bob Sulanke [32], who (in [32]) already says that my object 2) is one of the better-known Narayana-enumerated objects.
May 7, 2022 at 10:06 history answered Carlo Beenakker CC BY-SA 4.0