History of Catalan enumeration (source code)

= History of Catalan enumeration

<Leonhard Euler>'s 1751 correspondence already studied <triangulations of a convex polygon> and gave a closed formula for their counts. <Johann Andreas von Segner> supplied a combinatorial <recurrence relation> in a paper written in 1758. <Eugène Charles Catalan>'s nineteenth-century work connected the formula to bracketed products. This history, documented in <Igor Pak>'s account, shows how the same counting structure reappeared through different objects; the modern name alone does not establish discovery priority.<History of Catalan numbers by Igor Pak>[§§2–3 and §5, printed pp. 2–4: Euler correspondence, Segner recurrence and Catalan's bracketed products]{ref}