I became rather interested in the early history of Catalan numbers after reading multiple somewhat contradictory historical accounts. Now that I checked the sources, most of which are available online (see my Catalan Numbers page), I think I understand what happened. While I conclude that Euler deserve most of the credit, as I see it, what really happened is a bit more complicated. Basically, this is a story of research collaboration, only fragments of which are known.
Warning: I am assuming you are familiar with basic results on Catalan numbers, which allows me to concentrate on the story rather than the math.
All sources basically agree that Catalan numbers are named after Eugène Catalan (1814–1894), though they were computed by Leonhard Euler. There are several narratives in the literature, which are variations on the following statements, neither of which is really correct:
1. The problem was…
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