Enter a number to instantly calculate its Bell number value.
Calculate the Bell Number Bn = ?
Result
What Is a Bell Number?
In combinatorics, a Bell number represents the total number of ways to partition a set of \( n \) elements into non-empty subsets. Denoted as \( B(n) \), Bell numbers play a crucial role in combinatorics and number theory.
How to Calculate Bell Numbers?
Bell numbers can be calculated recursively or directly using the following relationships:
\( B(0) = 1 \)
Recursive Formula (for \( n \geq 1 \)):
\( B(n) = \sum_{k=0}^{n-1} \binom{n-1}{k} B(k) \)
Here, \( \binom{n-1}{k} \) represents the binomial coefficient.
Examples
Example 1: What is the Bell number \( B(8) \)?
Solution:
Calculate \( B(8) \)
\( B(8) = 877 \)
Example 2: How many ways can a set of 10 elements be partitioned into subsets?