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Results tagged with catalan-numbers
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user 19729
The Catalan numbers form the sequence of numbers starting 1,1,2,5,14,42,... with explicit formula $\frac{1}{n+1}\binom{2n}{n}$. It counts many combinatorial objects like planar binary trees, triangulations, noncrossing partitions, Dyck paths, etc. See https://oeis.org/A000108
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votes
Proofs of some combinatorial identities
It's not the formally published literature, but unless I'm mistaken, the last of your three identities appears in Stanley's list of bijective proof problems (dated 2009) as number 194. He says there …
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