Bell’s triangle

Bell’s triangle or Aitken’s array or Peirce triangle is a triangular arrangement of integers in which the top row has a single 1, and each subsequent row begins with the last number of the previous row, and each remaining number in a row is the sum of the number to the left to the number above left.

The first eight rows are:

These are listed in A011971 of Sloane’s OEIS.

The left outermost diagonal gives the Bell numbers (1, 2, 5, 15, 52, 203, 877, 4140, etc.) in order.

Title	Bell’s triangle
Canonical name	BellsTriangle
Date of creation	2013-03-22 16:49:16
Last modified on	2013-03-22 16:49:16
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	5
Author	PrimeFan (13766)
Entry type	Data Structure
Classification	msc 05A18
Classification	msc 11B73
Synonym	Bell triangle
Synonym	Aitken’s array
Synonym	Aitken array
Synonym	Peirce triangle
Synonym	Peirce’s triangle