[[File:PascalTriangleAnimated2.gif|thumb|upright=1|In Pascal's triangle, each number is the sum of the two numbers directly above it.]]In the <math>n</math>th row of Pascal's triangle, the <math>k</math>th entry is denoted <math>\tbinom nk</math>, pronounced "{{mvar|n}} choose {{mvar|k}}". For example, the topmost entry is <math>\tbinom 00 = 1</math>. With this notation, the construction of the previous paragraph may be written as
for any positive integer <math>n</math> and any integer <math>0 \le k \le n</math>.<ref>The binomial coefficient <math>\scriptstyle {n \choose k}</math> is conventionally set to zero if ''k'' is either less than zero or greater than ''n''.</ref> This recurrence for the binomial coefficients is known as [[Pascal's rule]].
== History ==
[[File:Yanghui triangle.gif|thumb|right|upright=1|[[Yang Hui]]'s triangle, as depicted by the Chinese using [[Counting rods|rod numerals]], appears in [[Jade Mirror of the Four Unknowns]], a mathematical work by [[Zhu Shijie]], dated 1303.]]
