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The triangular array whose right-hand diagonal sequence consists of Bell numbers. The Bell numbers can easily be calculated by creating the so-called Bell triangle, also called Aitken's array or the Peirce triangle after Alexander Aitken and Charles Sanders Peirce. [6] Start with the number one. Put this on a row by itself. (, =)
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 .
If x is a triangular number, a is an odd square, and b = a − 1 / 8 , then ax + b is also a triangular number. Note that b will always be a triangular number, because 8 T n + 1 = (2 n + 1) 2 , which yields all the odd squares are revealed by multiplying a triangular number by 8 and adding 1, and the process for b given a is an odd ...
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For instance, the number 25 in column k = 3 and row n = 5 is given by 25 = 7 + (3×6), where 7 is the number above and to the left of 25, 6 is the number above 25 and 3 is the column containing the 6.
The number of alternative assignments for a given number of workers, taking into account the choices of how many stages to use and how to assign workers to each stage, is an ordered Bell number. [29] As another example, in the computer simulation of origami , the ordered Bell numbers give the number of orderings in which the creases of a crease ...
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That is, let s be the lower triangular matrix of Stirling numbers of the first kind, whose matrix elements = (,). The inverse of this ... is the n-th Bell number