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,^[1] 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 Charles Sanders Peirce (1880) and including also Alexander Aitken (1933) and Cohn et al. (1962), and for that reason has also been called Aitken's array or the Peirce triangle.^[2]

^ According to Gardner (1978), this name was suggested by Jeffrey Shallit, whose paper about the same triangle was later published as Shallit (1980). Shallit in turn credits Cohn et al. (1962) for the definition of the triangle, but Cohn et al. did not name the triangle.
^ Sloane, N. J. A. (ed.). "Sequence A011971 (Aitken's array)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[1] According to Gardner (1978), this name was suggested by Jeffrey Shallit, whose paper about the same triangle was later published as Shallit (1980). Shallit in turn credits Cohn et al. (1962) for the definition of the triangle, but Cohn et al. did not name the triangle.

[oeis-2] Sloane, N. J. A. (ed.). "Sequence A011971 (Aitken's array)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

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