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mathematical analysis > calculus > sequence > integer sequence > binomial coefficient

mathematical analysis > combinatorics > binomial coefficient

algebra > combinatorics > binomial coefficient

Terme préférentiel

binomial coefficient

In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers $n \geq k \geq 0$ and is written ${\\displaystyle {\ binom {n}{k}}.}$ It is the coefficient of the $x k$ term in the polynomial expansion of the binomial power $(1 + x) n$ ; this coefficient can be computed by the multiplicative formula

${\\displaystyle {\inom {n}{k}}={\ rac {n\ imes (n-1)\ imes \\cdots \ imes (n-k+1)}{k\ imes (k-1)\ imes \\cdots \ imes 1}},}$

which using factorial notation can be compactly expressed as

${\\displaystyle {\inom {n}{k}}={\ rac {n!}{k!(n-k)!}}.}$

coefficient binomial

français
coefficient du binôme

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