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Bell triangle

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

This page exists due to the efforts of the following people:

Timur

Timur

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. That is, rightmost value of n-th row is the count of all possible partitions of a set of size n. The construction of Bell triangle is described below the calculator. Note that this calculator uses "big integers" library (see Tips and tricks #9: Big numbers), so you can build pretty large triangles.

PLANETCALC, Bell triangle

Bell triangle

Construction of the Bell triangle

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

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

Then, the next value in the row is calculated by adding the previous value in the row with the corresponding value from 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...

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Creative Commons Attribution/Share-Alike License 3.0 (Unported) PLANETCALC, Bell triangle

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