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 the
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 (Gardner 1992, p. 29). A reflected version is sometimes also considered (Knuth 2005, p. 28).
Numbering the rows by ,
2, ..., the sums of the numbers
in the th
row are
,
2, ..., the sums of the numbers
in the 
th
row are
is a Stirling number of the second
kind, giving the first few for 
, 2, ... as 1, 3, 10, 37, 151, ... (OEIS A005493).
This OEIS integer sequence indexes the same row
sums starting at 0.
