The Catalan numbers C(n) can be defined in several equivalent ways.
A formal definition is:
C(n) = (2n)!/(n!(n+1)!).
Another definition: C(n)
is the number of ways to insert n pairs of parentheses in an expression with n+1 terms.
For example, if n = 2 there are two ways: ((ab)c) or (a(bc)) ;
if n = 3 there are 5 ways:
((ab)(cd)) ,
(((ab)c)d) ,
((a(bc))d) ,
(a((bc)d)) ,
(a(b(cd))) .
Accordingly, C(2) = 2 and C(3) = 5.
The Catalan sequence is OEIS
A000108; in the
Online Encyclopedia of Integer Sequences
you can find lots of additional information and further references on Catalan numbers.
This online calculator computes the Catalan numbers C(n)
for input values 0 ≤ n ≤ 25000 in arbitrary precision arithmetic.
So, for example, you will get all 598 digits of C(1000) –
a very large number!
See also:
• 100+ digit calculator: arbitrary precision arithmetic
• Prime factorization calculator
• Binomial coefficients calculator
• Fibonacci numbers calculator
• Euler's totient function φ calculator
• Highly composite numbers
• Divisors and sumofdivisors calculator
