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

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

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

} 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...

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 {\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...

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...

+ 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...

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

theorem are the multinomial coefficients. They can be expressed in numerous ways, including as a product of binomial coefficients or of factorials: ( n k...

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

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

In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is...

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,...

appearing as multipliers for the terms in this expansion are the binomial coefficients two rows down from the top of Pascal's triangle. The expansion of...

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

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

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

OEIS Foundation. Retrieved 2016-05-31. "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia of...

In probability theory and statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), percent RMS, and...

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

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...

A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. The variables...

"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...

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

OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A000332 (Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24)". The On-Line Encyclopedia of...

{\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...

× 11 × 13, sphenic number, pentagonal number, pentatope number ( binomial coefficient ( 13 4 ) {\displaystyle {\tbinom {13}{4}}} ), Harshad number, member...

and preceding 127. As the binomial coefficient ( 9 4 ) {\displaystyle {\tbinom {9}{4}}} , 126 is a central binomial coefficient, and in Pascal's Triangle...