The Bell triangle, also called Aitken's array or the Peirce triangle (Knuth 2005, p. 28), is the number triangle obtained by
beginning the first row with the number one, and beginning subsequent rows with last
number of the previous row. Rows are filled out by adding the number in the preceding
column to the number above it (OEIS A011971).
The Bell numbers 1, 1, 2, 5, 15, ... (OEIS A000110)
are then given as the values in the first column.
The name "Bell triangle" was suggested to Gardner by J. Shallit. A reflected version is sometimes also considered (Knuth 2005, p. 28).