# Questions tagged [catalan-numbers]

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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### Generating functions for Hankel determinants of Catalan numbers

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### Generating Fuss-Catalan numbers using the regular Catalan number

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### Kernel of a matrix and the Catalan numbers

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### Generalization of Catalan numbers

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### Does this question have anything to do with Catalan numbers?

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### Dyck words and Catalan numbers

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### Reference request: colored Motzkin path interpretation of Catalan numbers

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### Reference request: recurrence relation for Catalan numbers

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### A bijective proof for the odd companion to Shapiro's Catalan convolution

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### Are the “generalized Catalan numbers” of Dumitrescu–Mulase the "moments" of some "multivariate Wigner semicircle distribution"?

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### Upper bounds for a sequence of integers

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### Looking for a combinatorial proof for an identity involving $q$-Catalan triangles

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### Looking for a combinatorial proof for a Catalan identity

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### A formula for this generating function that is similar to the $qt$-Catalan numbers

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### A conjecture about sums over partitions arising from Hilbert scheme of points

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### Reciprocity for fans of bounded Dyck paths

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### What's the dimension of the Lie algebra generated by transpositions on $n$ objects?

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### A generalisation of the Catalan numbers

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### Proof of certain $q$-identity for $q$-Catalan numbers

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### Seeking bijective proof of a recurrence for generalized Narayana numbers

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### Non-nesting matchings and Catalan numbers

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### Domination relationship between generalized Dyck Paths

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### Dyck paths weighted by height profile

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### A divisibility problem involving Catalan numbers

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### Coincidences between average Catalan tableaux

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### "Oddity" of $q$-Catalan polynomials: Part II

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### Oddity of generalized Catalan numbers: Part I

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### How to compute this series: $\sum_{k=0}^\infty \frac{C_k}{2^{2k+1}}$ [closed]

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### Products of Catalan numbers

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### Reference request: Catalan number of type B

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### Reference request for some determinants of binomial coefficients

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### A matrix identity related to Catalan numbers

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### Math journal publishing work related to combinatorics, probability, counting problems etc.?

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### Show a sequence of sums involving Catalan Numbers converges

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### Mysterious symmetry - in search for a bijection

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### Is the order on repeated exponentiation the Dyck order?

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### Curious Catalan convolutions

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### Some quotients of Hankel determinants

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### Proofs of some combinatorial identities

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### Number of tilting modules

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### Reference request: Heyting algebra structure on Catalan numbers

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### Distribution of the area statistic for Catalan paths

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### On generalized Catalan numbers

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### generating $q$-Catalan numbers

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### Does $q$-Catalan number count subspaces?

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### Intuition behind Hook Length Formula

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### Is there a combinatorial interpretation or bijective proof for this Catalan number identity?

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### genus zero permutation and noncrossing partition

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### Can we define the Mandelbrot set in terms of the generating function of the Catalan numbers?

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