Linked from

The 12 pages that link to Catalan number, each with the reason it gives.

• Binomial coefficientCompared with: Catalan counts often arise from subtracting invalid choices from binomial totals.

• Generating functionRelated: A quadratic equation for its generating function yields the Catalan numbers and their formula.

• Recurrence relationBroader topic: Their convolution recurrence expresses how a structure splits into smaller structures.

• Pascal's triangleRelated: They can be calculated from central binomial coefficients in the triangle.

• Binary treeRelated: Catalan numbers count distinct ordered binary-tree shapes with a fixed number of nodes.

• Combinatorial proofBroader topic: Their many interpretations let identities be proved by matching distinct families of objects.

• Integer sequenceRelated: The Catalan numbers exemplify sequences defined by combinatorial counting.

• Pascal's ruleRelated: Catalan recurrences combine binomial-coefficient identities related to Pascal's rule.

• Cayley's formulaCompared with: Catalan numbers count plane tree shapes, where branching order matters, unlike Cayley's abstract labeled trees.

• Lagrange inversion theoremBroader topic: Lagrange inversion extracts its generating-function coefficients from an implicit equation.

• Bertrand's ballot theoremRelated: Equal-vote ballot counts are governed by Catalan paths, a boundary case of ballot enumeration.

• Algebraic combinatoricsRelated: Its diverse interpretations invite algebraic generating functions and bijective explanations.