Bell triangle

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

Number of rows

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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...