# binomial coefficient

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Related to binomial coefficient: binomial theorem, binomial distribution

## binomial coefficient

[bī′nō·mē·əl kō·ə′fish·ənt]
(mathematics)
A coefficient in the expansion of (x + y) n , where n is a positive integer; the (k + 1)st coefficient is equal to the number of ways of choosing k objects out of n without regard for order. Symbolized (nk); nCk ; C (n,k); Cnk.
References in periodicals archive ?
All other negative binomial coefficients presented in table 2 are of the anticipated signs and are significantly different from zero with the exception of the coefficients for the destination country population variable.
d] with k cut-points is given by the binomial coefficient [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
n] (I) since it yields a signed binomial coefficient when [absolute value of I] = 1 and it originates from the additive formula (4.
The binomial coefficients in the expression (12) for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are now of the form
Remark 1: Also note that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] which is a binomial coefficient for each n [greater than or equal to] 1.
Our computation using the binomial coefficient can become forbidding even if the population size is modestly large.
where the right hand side denotes the classical binomial coefficient.
Solution to problem e1288: Odd binomial coefficients.
can be viewed as the number of ways to pick the non-circled chosen points from [m], and the binomial coefficient ([?
The q-binomial coefficient [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (also called the Gaussian polynomial) is a q-analog of the binomial coefficient ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]).
Finally, if d [greater than or equal to] 3 and d does not divide k, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the first q binomial coefficient vanishes for k [not equivalent to] 1 mod d, and the second one vanishes for k [equivalent to] 1 mod d.
q-analogs of the binomial coefficient congruences of Babbage, Wolstenholme and Glaisher.

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