The C5 = 42 noncrossing partitions of a 5-element set (below, the other 10 of the 52 partitions)
In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after the French-Belgian mathematician Eugène Charles Catalan.
The n-th Catalan number can be expressed directly in terms of the central binomial coefficients by
The first Catalan numbers for n = 0, 1, 2, 3, ... are
1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, ... (sequence A000108 in the OEIS).
named after the French-Belgian mathematician Eugène Charles Catalan. The n-th Catalannumber can be expressed directly in terms of the central binomial...
9 (1955) p. 120-121 [retrieved 2012-10-19] Weisstein, Eric W. "Catalan-Mersenne Number". MathWorld. "Questions proposées". Nouvelle correspondance mathématique...
up Catalan, Catalans, catalan, catalans, or catalán in Wiktionary, the free dictionary. Catalan may refer to: From, or related to Catalonia: Catalan language...
Catalan (/ˈkætələn, -æn/ KAT-ə-lən, -lan or /ˌkætəˈlæn/ KAT-ə-LAN; autonym: català, Eastern Catalan: [kətəˈla]), known in the Valencian Community and...
Catalans (Catalan, French and Occitan: catalans; Spanish: catalanes, Italian: catalani, Sardinian: cadelanos) are a Romance ethnic group native to Catalonia...
third Catalannumber and the third Sophie Germain prime. Notably, 5 is equal to the sum of the only consecutive primes 2 + 3 and it is the only number that...
The Catalan independence movement (Catalan: independentisme català; Spanish: independentismo catalán; Occitan: independentisme catalan) is a social and...
neighbor vertices. The total number of ways to triangulate a convex n-gon by non-intersecting diagonals is the (n−2)nd Catalannumber, which equals n ( n + 1...
The Catalan Countries (Catalan: Països Catalans, Eastern Calatan: [pəˈizus kətəˈlans]) are those territories where the Catalan language is spoken. They...
The 2024 Catalan regional election will be held on Sunday, 12 May 2024, to elect the 14th Parliament of the autonomous community of Catalonia. All 135...
The Catalan Opening is a chess opening where White plays d4 and c4 and fianchettoes the white bishop on g2. A common opening sequence is 1.d4 Nf6 2.c4...
The Catalan Atlas (Catalan: Atles català, Eastern Catalan: [ˈatləs kətəˈla]) is a medieval world map, or mappa mundi, probably created in the late 1370s...
the Institut d'Estudis Catalans (IEC) regulates the spoken standard based on Central Catalan, which has the highest number of speakers and is spoken...
parenthesization of a product of n matrices?" The number of possible parenthesizations is given by the (n–1)th Catalannumber, which is O(4n / n3/2), so checking each...
include Peirce (1880) and Aitken (1933). Touchard polynomials Catalannumber Stirling number Stirling numbers of the first kind Gardner 1978. Halmos, Paul...
Valencian Community of Spain to refer to the Romance language also known as Catalan, either as a whole or in its Valencia-specific linguistic forms. The Valencian...
Catalan Bay (Spanish: La Caleta) is a bay and fishing village in Gibraltar, on the eastern side of The Rock away from Westside. Although the origin of...
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