# Bell triangle

This online calculator constructs the Bell triangle for the given number of rows.

### Esta página existe graças aos esforços das seguintes pessoas:

#### Timur

Criado: 2019-12-22 13:21:44, Ultima atualização: 2021-03-19 20:52:54

The calculator constructs the Bell triangle for the given number of rows. The values of the triangle elements count partitions of a set in which a given triangle element is the largest singleton1. The rightmost value of each row is the Bell number for a set of size n, where n is a row number, starting from 1. The rightmost value of n-th row is the count of all possible partitions of a set of size n. The construction of the Bell triangle is described below the calculator. Note that this calculator uses the "big integers" library (see Tips and tricks #9: Big numbers), so you can build pretty large triangles.

#### Bell triangle

The file is very large. Browser slowdown may occur during loading and creation.

### Construction of the Bell triangle

The number 1 is placed in the first position of the first row.
Row 1: 1

Each next row starts by copying the rightmost value of the previous row.
Row 1: 1
Row 2: 1

The next value in the row is calculated by adding the previous value in the row with the corresponding value from the previous row.
Row 1: 1
Row 2: 1 2(1+1)

Then
Row 1: 1
Row 2: 1 2
Row 3: 2 3(1+2) 5(2+3)

And so on...

URL copiado para a área de transferência
PLANETCALC, Bell triangle