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Catalan number — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Catalan_number
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T21:35:53.957Z
SHA-256 of the archived text: 81d0286b0af73e6d0edcd57a551d130fc1624485fab2a223a9a2c8212e9abc18
Stable URL of this page: https://metraipolis.com/documento/dc_2ef6dcd07d33

How to cite

Catalan number — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Catalan_number (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_2ef6dcd07d33 (Metraipolis archive dc_2ef6dcd07d33, sha256 81d0286b0af73e6d0edcd57a551d130fc1624485fab2a223a9a2c8212e9abc18)

BibTeX

@misc{dc2ef6dcd07d33,
  title = {Catalan number — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Catalan_number},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_2ef6dcd07d33; sha256 81d0286b0af73e6d0edcd57a551d130fc1624485fab2a223a9a2c8212e9abc18},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Catalan_number. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after Eugène Catalan, though they were previously discovered in the 1730s by Minggatu. The n-th Catalan number can be expressed directly in terms of the central binomial coefficients by C n = 1 n + 1 ( 2 n n ) = ( 2 n ) ! ( n + 1 ) ! n ! for n ≥ 0. {\displaystyle C_{n}={\frac {1}{n+1}}{2n \choose n}={\frac {(2n)!}{(n+1)!\,n!}}\qquad {\text{for }}n\geq 0.} 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).

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «combinatorics»).
Fonte: Wikipedia in inglese, voce «Catalan number» — https://en.wikipedia.org/wiki/Catalan_number
Wikidata Q270513 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q270513
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Catalan_number?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1375551910, consultata il 2026-10-07T21:06:56.352Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 1cf73d9426a782b2f4b3593fbcc3511bffe670a4095045d73503629c2fe50d01