mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed...

} The coefficient ⁠ a {\displaystyle a} ⁠ in each term ⁠ a x k y m {\displaystyle \textstyle ax^{k}y^{m}} ⁠ is known as the binomial coefficient ⁠ ( n...

Gaussian binomial coefficients (also called Gaussian coefficients, Gaussian polynomials, or q-binomial coefficients) are q-analogs of the binomial coefficients...

In mathematics the nth central binomial coefficient is the particular binomial coefficient ( 2 n n ) = ( 2 n ) ! ( n ! ) 2  for all  n ≥ 0. {\displaystyle...

the right-hand side is expressed in terms of the (generalized) binomial coefficients ( α k ) = α ( α − 1 ) ( α − 2 ) ⋯ ( α − k + 1 ) k ! . {\displaystyle...

positive covariance term. The term "negative binomial" is likely due to the fact that a certain binomial coefficient that appears in the formula for the probability...

! {\displaystyle {\binom {n}{k}}={\frac {n!}{k!(n-k)!}}} is the binomial coefficient. The formula can be understood as follows: pk qn−k is the probability...

v=x_{1}e_{1}+x_{2}e_{2}+\dotsb +x_{n}e_{n}.} Correlation coefficient Degree of a polynomial Monic polynomial Binomial coefficient "ISO 80000-1:2009". International Organization...

+ 19 is the seventh square number, 49. 70 is the fourth central binomial coefficient, preceding { 1 , 2 , 6 , 20 } {\displaystyle \{1,2,6,20\}} , as the...

mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics,...

Bhargava factorial Binomial coefficient Pascal's triangle Binomial distribution Binomial proportion confidence interval Binomial-QMF (Daubechies wavelet...

{\displaystyle C(n,k)} or C k n {\displaystyle C_{k}^{n}} , is equal to the binomial coefficient ( n k ) = n ( n − 1 ) ⋯ ( n − k + 1 ) k ( k − 1 ) ⋯ 1 , {\displaystyle...

function for binomial coefficients for a fixed n, one may ask for a bivariate generating function that generates the binomial coefficients (n k) for all...

number p that divides a given binomial coefficient. In other words, it gives the p-adic valuation of a binomial coefficient. The theorem is named after...

partition yields a partition of n − M into at most M parts. The Gaussian binomial coefficient is defined as: ( k + ℓ ℓ ) q = ( k + ℓ k ) q = ∏ j = 1 k + ℓ ( 1...

Like the binomial distribution that involves binomial coefficients, there is a negative binomial distribution in which the multiset coefficients occur....

n − 1 ) 2 {\displaystyle {n \choose 2}={n(n-1) \over 2}} is the binomial coefficient for the number of ways to choose two items from n items. The number...

In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential...

distinguishable bins. The solution to this particular problem is given by the binomial coefficient ( n + k − 1 k − 1 ) {\displaystyle {\tbinom {n+k-1}{k-1}}} , which...

example of a multidimensional recurrence relation is given by the binomial coefficients ( n k ) {\displaystyle {\tbinom {n}{k}}} , which count the ways...

Bernoulli number, and ( p k ) {\displaystyle {\binom {p}{k}}} is a binomial coefficient. In the following summations, a is assumed to be different from 1...

( N , M , n ) {\displaystyle p(N,M,n)} is the following Gaussian binomial coefficient: ∑ n = 0 ∞ p ( N , M , n ) q n = ( N + M M ) q = ( 1 − q N + M )...

Pascal's formula) is a combinatorial identity about binomial coefficients. The binomial coefficients are the numbers that appear in Pascal's triangle. Pascal's...

contains the binomial coefficients that appear in the binomial expansion and the binomial distribution. The binomial and trinomial coefficients, expansions...

of the terms in that sum. It is the generalization of the binomial theorem from binomials to multinomials. For any positive integer m and any non-negative...

powerful insights into each or both of the sets. The symmetry of the binomial coefficients states that ( n k ) = ( n n − k ) . {\displaystyle {n \choose k}={n...

Look up binomial in Wiktionary, the free dictionary. Binomial may refer to: Binomial (polynomial), a polynomial with two terms Binomial coefficient, numbers...

) {\displaystyle {n \choose k}} is a binomial coefficient. Bernoulli trials may also lead to negative binomial distributions (which count the number...

"mistake" actually gives the correct result, since p divides all the binomial coefficients apart from the first and the last, making all the intermediate terms...

In combinatorics, the binomial transform is a sequence transformation (i.e., a transform of a sequence) that computes its forward differences. It is closely...