Explore: Catalan Numbers

The Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named

famous Catalan's conjecture, which was eventually proved in 2002; and introducing the Catalan numbers to solve a combinatorial problem. Catalan was born

In combinatorial mathematics and statistics, the Fuss–Catalan numbers are numbers of the form A m ( p , r ) ≡ r m p + r ( m p + r m ) = r m ! ∏ i = 1

{1}{1}}\right)^{n}=n^{2}.} The ordinary generating function for the Catalan numbers is G ( C n ; x ) = 1 − 1 − 4 x 2 x . {\displaystyle G(C_{n};x)={\frac

up Catalan, Catalans, catalan, catalans, or catalán in Wiktionary, the free dictionary. Catalan may refer to: From, or related to Catalonia: Catalan language

Schröder numbers, or the Hipparchus numbers, after Eugène Charles Catalan and his Catalan numbers, Ernst Schröder and the closely related Schröder numbers, and

{\displaystyle c_{n+1}=2^{c_{n}}-1=M_{c_{n}}} is called the sequence of Catalan–Mersenne numbers. The first terms of the sequence (sequence A007013 in the OEIS)

p is a Wieferich prime, then p2 is a Catalan pseudoprime. Aebi, Christian; Cairns, Grant (2008). "Catalan numbers, primes and twin primes" (PDF). Elemente

1730s, he first established and used what was later to be known as Catalan numbers. The Jesuit missionaries' influence can be seen by many traces of European

valid sequence of balanced parentheses. Lobb numbers form a natural generalization of the Catalan numbers, which count the complete strings of balanced