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Bell triangle

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

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This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/8527/. Also, please do not modify any references to the original work (if any) contained in this content.

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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