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• Binomial_coefficient abstract "In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the binomial coefficient indexed by n and k is usually written . It is the coefficient of the x k term in the polynomial expansion of the binomial power (1 + x) n. Under suitable circumstances the value of the coefficient is given by the expression . Arranging binomial coefficients into rows for successive values of n, and in which k ranges from 0 to n, gives a triangular array called Pascal's triangle.This family of numbers also arises in many areas of mathematics other than algebra, notably in combinatorics. For any set containing n elements, the number of distinct k-element subsets of it that can be formed (the k-combinations of its elements) is given by the binomial coefficient . Therefore is often read as "n choose k". The properties of binomial coefficients have led to extending the meaning of the symbol beyond the basic case where n and k are nonnegative integers with k ≤ n; such expressions are then still called binomial coefficients.The notation was introduced by Andreas von Ettingshausen in 1826, although the numbers were already known centuries before that (see Pascal's triangle). The earliest known detailed discussion of binomial coefficients is in a tenth-century commentary, by Halayudha, on an ancient Sanskrit text, Pingala's Chandaḥśāstra. In about 1150, the Indian mathematician Bhaskaracharya gave an exposition of binomial coefficients in his book Lilavati.Alternative notations include C(n, k), nCk, nCk, Ckn, Cnk, Cn,k in all of which the C stands for combinations or choices.".
• Binomial_coefficient thumbnail Pascal's_triangle_5.svg?width=300.
• Binomial_coefficient wikiPageExternalLink toppage.html.
• Binomial_coefficient wikiPageExternalLink komb.php?language=english.
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• Binomial_coefficient hasPhotoCollection Binomial_coefficient.
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• Binomial_coefficient id "p/b016410".
• Binomial_coefficient title "Binomial Coefficient".
• Binomial_coefficient title "Binomial coefficients".
• Binomial_coefficient title "Bounds for binomial coefficients".
• Binomial_coefficient title "Generalized binomial coefficients".
• Binomial_coefficient title "Proof that C is an integer".
• Binomial_coefficient subject Category:Combinatorics.
• Binomial_coefficient subject Category:Factorial_and_binomial_topics.
• Binomial_coefficient subject Category:Integer_sequences.
• Binomial_coefficient subject Category:Triangles_of_numbers.
• Binomial_coefficient type Abstraction100002137.
• Binomial_coefficient type Arrangement107938773.
• Binomial_coefficient type Attribute100024264.
• Binomial_coefficient type Figure113862780.
• Binomial_coefficient type Group100031264.
• Binomial_coefficient type IntegerSequences.
• Binomial_coefficient type Ordering108456993.
• Binomial_coefficient type PlaneFigure113863186.
• Binomial_coefficient type Polygon113866144.
• Binomial_coefficient type Sequence108459252.
• Binomial_coefficient type Series108457976.
• Binomial_coefficient type Shape100027807.
• Binomial_coefficient type Triangle113879320.
• Binomial_coefficient type TrianglesOfNumbers.
• Binomial_coefficient comment "In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the binomial coefficient indexed by n and k is usually written . It is the coefficient of the x k term in the polynomial expansion of the binomial power (1 + x) n. Under suitable circumstances the value of the coefficient is given by the expression .".
• Binomial_coefficient label "Binomiaalcoëfficiënt".
• Binomial_coefficient label "Binomial coefficient".
• Binomial_coefficient label "Binomialkoeffizient".
• Binomial_coefficient label "Coefficient binomial".
• Binomial_coefficient label "Coefficiente binomiale".
• Binomial_coefficient label "Coeficiente binomial".
• Binomial_coefficient label "Coeficiente binomial".
• Binomial_coefficient label "Symbol Newtona".
• Binomial_coefficient label "Биномиальный коэффициент".
• Binomial_coefficient label "معامل ثنائي".
• Binomial_coefficient label "二項式係數".
• Binomial_coefficient sameAs Kombinační_číslo.
• Binomial_coefficient sameAs Binomialkoeffizient.
• Binomial_coefficient sameAs Coeficiente_binomial.
• Binomial_coefficient sameAs Koefiziente_binomial.
• Binomial_coefficient sameAs Coefficient_binomial.
• Binomial_coefficient sameAs Coefficiente_binomiale.
• Binomial_coefficient sameAs 이항계수.
• Binomial_coefficient sameAs Binomiaalcoëfficiënt.
• Binomial_coefficient sameAs Symbol_Newtona.
• Binomial_coefficient sameAs Coeficiente_binomial.
• Binomial_coefficient sameAs m.01h7m.
• Binomial_coefficient sameAs Q209875.
• Binomial_coefficient sameAs Q209875.
• Binomial_coefficient sameAs Binomial_coefficient.
• Binomial_coefficient wasDerivedFrom Binomial_coefficient?oldid=605428380.
• Binomial_coefficient depiction Pascal's_triangle_5.svg.
• Binomial_coefficient isPrimaryTopicOf Binomial_coefficient.