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I was reading about Catalan numbers and how they provide the number count in a variety of situations.

I found it very interesting how the main proof is about the underlying common patterns and symmetry of problems that appear very different e.g. well formed parenthesis, lattice paths, mountains and trees etc.

I think Catalan only formally introduced so I was wondering if we know how far back they were known and how the first proofs/interpretations were inspired?

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    $\begingroup$ Did you look at the references in the Wikipedia article on Catalan numbers? Also, the top hit of the first google search I tried, namely Catalan + number + Euler, was History of Catalan numbers by Igor Pak -- appendix to Richard Stanley's 2015 book Catalan Numbers. See also the links at this web page maintained by Pak. $\endgroup$ Apr 27 at 20:46
  • $\begingroup$ @DaveLRenfro: Yes I have seen wikipedia but it is very brief mentioning. Since whereI read about them they were also parallel with other problems I was looking for something that shows how those interpretation came about. But may be those came later $\endgroup$
    – Jim
    Apr 27 at 21:07
  • $\begingroup$ Note that I said references in the Wikipedia article. And obviously, you'll want to look at their references, and the references of the references of the references, and so on. Since not all of these are likely to be freely available on the internet, you may have to visit a nearby university library (and maybe you don't have time to drive to one until the weekend), probably visit several times because you don't want to waste your time there reading stuff (you can do that at home) but instead spend all of your presumably valuable time photocopying and downloading everything of interest. $\endgroup$ Apr 27 at 21:17

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