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'''Pascal's triangle''' is a convenient tabular representation of the [[binomial coefficient]]s. Already known in the 11th century,<ref>[http://www-gap.dcs.st-and.ac.uk is the ''k''th binomial coefficient in the [[binomial expansion]] of <math>\scriptstyle (x + y)^n</math>, then

|[[Binomial coefficient]]

...the style of the proof, e.g., converted some factorial expressions to the binomial coefficient, moved the Kroneker delta around and moved some factorials out of parenthes

...tion is found in many combinatorial counting problems. For example, the [[binomial coefficient]]s, which count the number of subsets size ''r'' drawn from a set of ''n''

...tion of factorials, the most important example perhaps being that of the [[binomial coefficient]] ...ies of the gamma function when extended to negative numbers are natural. A binomial coefficient gives the number of ways to choose <math>k</math> elements from a set of <m

{{pl|Binomial coefficient}} -