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Results tagged with catalan-numbers
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user 36823
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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Higher-dimensional Catalan numbers?
One relatively direct generalization is to interpret the $n$-th Catalan number as the multiplicity of the trivial representation in the $2n$-th tensor power of the standard $2$-dimensional representat …
