Bell Triangle Calculator

Welcome to the Bell Triangle Calculator, which can help you quickly build a Bell triangle.

A Bell triangle is a triangle of numbers similar to Pascal’s triangle. The values of numbers count the different partitions in the set in which a given element is the most significant singleton element. It is closely connected to the Bell numbers found on either side of the triangle. These are named after Eric Temple Bell. Many authors have contributed to the Bell triangle. Sanders Peirce made important contributions in 1880 and Alexander Aitken in 1933. So, a Bell triangle is also called a Peirce triangle or Aitken’s array.

To construct a Bell triangle, start with the number one. Each element in a row is formed by adding the number in the predecessor column along with the number above. The first element of each row is the last number in the previous row.

So a Bell triangle is

1

1     2

2     3     5

5     7     10    15

15   17   27    37     52

And so on.

In triangular form, it can be written as:

Bell numbers are 1, 1, 2, 5, 15 and etc, which are the first numbers in each column of the Bell triangle.

The procedure to use the Bell triangle calculator is as follows: