Bell Numbers Calculator

Calculate the number of ways to partition a set

Result

B(n)
=
-

About Bell Numbers

Bell numbers, denoted as B(n), count the total number of ways to partition a set of n elements into non-empty subsets.

For example, B(3) = 5 because a set of 3 elements can be partitioned in 5 different ways:

  • {1,2,3}
  • {1,2},{3}
  • {1,3},{2}
  • {2,3},{1}
  • {1},{2},{3}

Bell numbers can be calculated using the Bell Triangle, similar to Pascal's Triangle.

Note: Bell numbers grow very quickly. For large values of n, the result might be too large to be displayed accurately.