Catalan Number
In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after the Belgian mathematician Eugène Charles Catalan (1814–1894).
The nth Catalan number is given directly in terms of 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, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, … (sequence A000108 in OEIS)
Read more about Catalan Number: Properties, Applications in Combinatorics, Proof of The Formula, Hankel Matrix, Quadruple Factorial, History
Famous quotes containing the words catalan and/or number:
“The table kills more people than war does.”
—Catalan proverb, quoted in Colman Andrews, Catalan Cuisine.
“Love has its name borrowed by a great number of dealings and affairs that are attributed to it—in which it has no greater part than the Doge in what is done at Venice.”
—François, Duc De La Rochefoucauld (1613–1680)