Nth Catalan Number Calculator

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✖Value of N is any natural number or positive integer that can be used for combinatorial calculations.ⓘ Value of N [n]

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✖Nth Catalan Number is the nth number in Catalan numbers, which are a sequence of natural numbers that occur in various counting problems.ⓘ Nth Catalan Number [C_n]

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Formula

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Nth Catalan Number

Formula

`"C"_{"n"} = (1/("n"+1))*C(2*"n","n")`

Example

`"1430"=(1/("8"+1))*C(2*"8","8")`

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Nth Catalan Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Nth Catalan Number = (1/(Value of N+1))*C(2*Value of N,Value of N)
C_n = (1/(n+1))*C(2*n,n)
This formula uses 1 Functions, 2 Variables

Functions Used

C - In combinatorics, the binomial coefficient is a way to represent the number of ways to choose a subset of objects from a larger set. It is also known as the "n choose k" tool., C(n,k)

Variables Used

Nth Catalan Number - Nth Catalan Number is the nth number in Catalan numbers, which are a sequence of natural numbers that occur in various counting problems.
Value of N - Value of N is any natural number or positive integer that can be used for combinatorial calculations.

STEP 1: Convert Input(s) to Base Unit

Value of N: 8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_n = (1/(n+1))*C(2*n,n) --> (1/(8+1))*C(2*8,8)

Evaluating ... ...

C_n = 1430

STEP 3: Convert Result to Output's Unit

1430 --> No Conversion Required

FINAL ANSWER

1430 <-- Nth Catalan Number

(Calculation completed in 00.004 seconds)

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Created by Devendar Kachhwaha

Indian Institute of technology (IIT-BHU), Varanasi

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Verified by Katakam Devaharsha Siva Sai

Sri Sathya Sai Institute of Higher Learning (SSSIHL), Prasanthi Nilayam

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< 14 Combinations Calculators

No of Combinations of N Different Things taken R at once given M Specific Things Always Occur

Go Number of Combinations = C((Value of N-Value of M),(Value of R-Value of M))

No of Combinations of (P+Q) Things into Two Groups of P and Q Things

Go Number of Combinations = ((Value of P+Value of Q)!)/((Value of P!)*(Value of Q!))

nCr or C(n,r)

Go Number of Combinations = (Value of N!)/(Value of R!*(Value of N-Value of R)!)

No of Combinations of N Identical Things into R Different Groups if Empty Groups are Allowed

Go Number of Combinations = C(Value of N+Value of R-1,Value of R-1)

Nth Catalan Number

Go Nth Catalan Number = (1/(Value of N+1))*C(2*Value of N,Value of N)

No of Combinations of N Different Things taken R at once and Repetition Allowed

Go Number of Combinations = C((Value of N+Value of R-1),Value of R)

No of Combinations of N Different Things taken R at once given M Specific Things Never Occur

Go Number of Combinations = C((Value of N-Value of M),Value of R)

No of Combinations of N Different Things, P and Q Identical Things taken Atleast One at once

Go Number of Combinations = (Value of P+1)*(Value of Q+1)*(2^Value of N)-1

Maximum Value of nCr when N is Odd

Go Number of Combinations = C(Value of N (Odd),(Value of N (Odd)+1)/2)

No of Combinations of N Identical Things into R Different Groups if Empty Groups are Not Allowed

Go Number of Combinations = C(Value of N-1,Value of R-1)

Maximum Value of nCr when N is Even

Go Number of Combinations = C(Value of N,Value of N/2)

No of Combinations of N Different Things taken R at once

Go Number of Combinations = C(Value of N,Value of R)

No of Combinations of N Different Things taken Atleast One at once

Go Number of Combinations = 2^(Value of N)-1

No of Combinations of N Identical Things taken Zero or more at once

Go Number of Combinations = Value of N+1

Nth Catalan Number Formula

Nth Catalan Number = (1/(Value of N+1))*C(2*Value of N,Value of N)
C_n = (1/(n+1))*C(2*n,n)

What are Combinations?

In combinatorics, Combinations refer to the different ways of selecting a subset of items from a larger set without regard to the order of selection. Combinations are used to count the number of possible outcomes when the order of selection does not matter. For example, if you have a set of three elements {A, B, C}, the Combinations of size 2 would be {AB, AC, BC}. In this case, the order of the items within each combination does not matter, so {AB} and {BA} are considered the same combination.

The number of Combinations of selecting "k" items from a set of "n" items is denoted as C(n, k). It is calculated using the binomial coefficient formula: C(n, k) = n! / (k! * (n - k)!)

Combinations have various applications in mathematics, probability theory, statistics, and other fields.

What are the properties of Catalan Numbers?

Catalan Numbers have many interesting properties and appear in a wide range of combinatorial problems. Some examples include:

1. Counting the number of full binary trees with n+1 leaves (n-th Catalan Number).
2. Count the number of ways to parenthesize a product of n+1 factors (n-th Catalan Number).
3. Counting the number of non-isomorphic ordered trees with n+1 vertices (n-th Catalan Number).

How to Calculate Nth Catalan Number?

Nth Catalan Number calculator uses Nth Catalan Number = (1/(Value of N+1))*C(2*Value of N,Value of N) to calculate the Nth Catalan Number, Nth Catalan Number formula is defined as the nth number in Catalan numbers, which are a sequence of natural numbers that occur in various counting problems. Nth Catalan Number is denoted by C_n symbol.

How to calculate Nth Catalan Number using this online calculator? To use this online calculator for Nth Catalan Number, enter Value of N (n) and hit the calculate button. Here is how the Nth Catalan Number calculation can be explained with given input values -> 429 = (1/(8+1))*C(2*8,8).

FAQ

What is Nth Catalan Number?

Nth Catalan Number formula is defined as the nth number in Catalan numbers, which are a sequence of natural numbers that occur in various counting problems and is represented as C_n = (1/(n+1))*C(2*n,n) or Nth Catalan Number = (1/(Value of N+1))*C(2*Value of N,Value of N). Value of N is any natural number or positive integer that can be used for combinatorial calculations.

How to calculate Nth Catalan Number?

Nth Catalan Number formula is defined as the nth number in Catalan numbers, which are a sequence of natural numbers that occur in various counting problems is calculated using Nth Catalan Number = (1/(Value of N+1))*C(2*Value of N,Value of N). To calculate Nth Catalan Number, you need Value of N (n). With our tool, you need to enter the respective value for Value of N and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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