An Introduction to Enumeration pp 79-105 | Cite as
Matrices, Sequences and Sums
Chapter
Abstract
This triangle – better described as an array – is associated with the Binomial Theorem 2.1; this expresses the powers of (1+z) in terms of successive powers of z: The next result shows that the coefficients involved represent the number of ways of choosing k elements from r, as assumed in the first chapter.
$$(1+z)^r=\sum\limits_{k\ge 0}\binom{r}{k}z^k.$$
Keywords
Eulerian Number Fibonacci Number Lower Triangular Matrix Binomial Theorem Lucas Number
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer-Verlag London Limited 2011