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...

{\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...

+ 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...

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...

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...

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

! {\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...

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

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

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

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...

binomial tree of order k {\displaystyle k} has ( k d ) {\displaystyle {\tbinom {k}{d}}} nodes at depth d {\displaystyle d} , a binomial coefficient....

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...

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...

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...

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...

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...

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...

( 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 )...

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

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...

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

theory, Lucas's theorem expresses the remainder of division of the binomial coefficient ( m n ) {\displaystyle {\tbinom {m}{n}}} by a prime number p in terms...

contains the binomial numbers and relates to the binomial expansion and the binomial distribution. The binomial and trinomial numbers, coefficients, expansions...

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