Catalan numbers and lattice paths

The Catalan family of counting sequences and the lattice paths they count: Catalan, Fuss–Catalan, Narayana, Motzkin, Schröder, Fine and Riordan numbers, Dyck and Motzkin paths and their statistics, Delannoy numbers and walks with prescribed steps, including arithmetic properties (parity, integrality, perfect powers) of these numbers.

• Catalan numbers and their generalizations
• Motzkin numbers and Motzkin paths
• Dyck paths and lattice walks

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