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Nth Catalan Number Formula

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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. Check FAQs

C n = (\frac{1}{n + 1}) \cdot C (2 \cdot n, n)

C_n - Nth Catalan Number?n - Value of N?

Nth Catalan Number Example

With values

With units

Only example

Here is how the Nth Catalan Number equation looks like with Values.

Here is how the Nth Catalan Number equation looks like with Units.

Here is how the Nth Catalan Number equation looks like.

1430 = (\frac{1}{8 + 1}) \cdot C (2 \cdot 8, 8)

1430 = (\frac{1}{8 + 1}) \cdot C (2 \cdot 8, 8)

1430 = (\frac{1}{8 + 1}) \cdot C (2 \cdot 8, 8)

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Nth Catalan Number Solution

Follow our step by step solution on how to calculate Nth Catalan Number?

FIRST Step Consider the formula

C n = (\frac{1}{n + 1}) \cdot C (2 \cdot n, n)

Next Step Substitute values of Variables

∴

C n = (\frac{1}{8 + 1}) \cdot C (2 \cdot 8, 8)

Next Step Prepare to Evaluate

∴

C n = (\frac{1}{8 + 1}) \cdot C (2 \cdot 8, 8)

LAST Step Evaluate

∴

C n = 1430

Nth Catalan Number Formula Elements

Variables

Functions

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.

Symbol: C_n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Nth Catalan Number

Value of N

Value of N is any natural number or positive integer that can be used for combinatorial calculations.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Value of N

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.

Syntax: C(n,k)

Other formulas in Combinations category

Go No of Combinations of N Different Things taken R at once

C = C (n, r)

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

C = C ((n + r - 1), r)

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

C = C (\begin{matrix} n - m \\ r - m \end{matrix})

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

C = C ((n - m), r)

How to Evaluate Nth Catalan Number?

Nth Catalan Number evaluator uses Nth Catalan Number = (1/(Value of N+1))*C(2*Value of N,Value of N) to evaluate 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 evaluate Nth Catalan Number using this online evaluator? To use this online evaluator for Nth Catalan Number, enter Value of N (n) and hit the calculate button.

FAQs on Nth Catalan Number

What is the formula to find Nth Catalan Number?

The formula of Nth Catalan Number is expressed as Nth Catalan Number = (1/(Value of N+1))*C(2*Value of N,Value of N). Here is an example- 429 = (1/(8+1))*C(2*8,8).

How to calculate Nth Catalan Number?

With Value of N (n) we can find Nth Catalan Number using the formula - Nth Catalan Number = (1/(Value of N+1))*C(2*Value of N,Value of N). This formula also uses Binomial Coefficient (C) function(s).

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