Bell triangle
In mathematics, the Bell triangle is a triangle of numbers analogous to Pascal's triangle, whose values count partitions of a set in which a given element is the largest singleton. It is named for its close connection to the Bell numbers, which may be found on both sides of the triangle, and which are in turn named after Eric Temple Bell. The Bell triangle has been discovered independently by multiple authors, beginning with and including also and , and for that reason has also been called Aitken's array or the Peirce triangle. Values Different sources give the same triangle in different orientations, some flipped from each other. In a format similar to that of Pascal's triangle, and in the order listed in the Online Encyclopedia of Integer Sequences, its first few rows are: 1 1 2 2 3 5 5 7 10 15 15 20 27 37 52 52 67 87 114 151 203 203 255 322 409 523 674 877 Construction The Bell triangle may be constructed by placing the number 1 in its first position. After that placement, the leftmost value in each row of the triangle is filled by copying the rightmost value in the previous row.