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New posts in catalan-numbers
An identity involving Catalan numbers and binomial coefficients.
combinatorics
summation
catalan-numbers
Catalan numbers: bijection between applications of a binary operator and Dyck words.
sequences-and-series
combinatorics
permutations
combinatorial-proofs
catalan-numbers
How to deal with this double summation?
summation
binomial-coefficients
catalan-numbers
lagrange-inversion
Combinatorics Identity about Catalan numbers: $\sum_{k=0}^n \frac{1}{k+1}\binom{2k}k \binom{2n-2k}{n-k}=\binom{2n+1}n$
combinatorics
summation
binomial-coefficients
catalan-numbers
combinatorial-proofs
Proving this identity $\sum_k\frac{1}{k}\binom{2k-2}{k-1}\binom{2n-2k+1}{n-k}=\binom{2n}{n-1}$ using lattice paths
combinatorics
binomial-coefficients
integer-lattices
catalan-numbers
Prove a combinatorial identity: $ \sum_{n_1+\dots+n_m=n} \prod_{i=1}^m \frac{1}{n_i}\binom{2n_i}{n_i-1}=\frac{m}{n}\binom{2n}{n-m}$
combinatorics
binomial-coefficients
catalan-numbers
Number of ways to pair off $2n$ points such that no chords intersect
combinatorics
discrete-mathematics
recurrence-relations
catalan-numbers
Identity with Catalan numbers
combinatorics
catalan-numbers
Finding relatives of the series $\varphi =\frac{3}{2}+\sum_{k=0}^{\infty}(-1)^{k}\frac{(2k)!}{(k+1)!k!2^{4k+3}}$.
sequences-and-series
catalan-numbers
golden-ratio
constants
Cashier has no change... catalan numbers.. probability question
probability
catalan-numbers
Generating function of $f(n) = C_n - \sum_{k=1}^{n-1}\binom{n}{k}f(n-k)$
combinatorics
discrete-mathematics
generating-functions
catalan-numbers
Using the Catalan numbers
catalan-numbers
Closed form for $ S(m) = \sum_{n=1}^\infty \frac{2^n \cdot n^m}{\binom{2n}n} $ for integer $m$?
taylor-expansion
riemann-zeta
hypergeometric-function
pattern-recognition
catalan-numbers
How do the Catalan numbers turn up here?
combinatorics
algorithms
catalan-numbers
Simplifying Catalan number recurrence relation
combinatorics
computer-science
catalan-numbers
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