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.
Our computation using the binomial coefficient
can become forbidding even if the population size is modestly large.
d] with k cut-points is given by the binomial coefficient
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
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.
where the right hand side denotes the classical binomial coefficient
Just as with ordinary binomial coefficients
, q-binomial coefficients
have multiple combinatorial interpretations and satisfy many identities, a few of which are highlighted below.
denote the usual q-analogs of numbers, factorials and binomial coefficients
Keywords: Hankel determinants, binomial coefficients
, almost product form evaluations, differential equations, [gamma]-operators.
A Maple calculation for n = 1000 of the binomial coefficient
ration above gives 0.
The terms [alpha] and [beta] are typical expressions to which 'Rice's method' can be applied, due to the presence of the binomial coefficient
inside an alternating sum.
In order to gain a sense of the magnitude of these effects, the negative binomial coefficients
can be transformed into incidence rate ratios.
The first is the right-circulant determinant sequence with binomial coefficients
and the second is the left-circulant determinant sequence with binomial coefficients
Among the topics are counting and proofs, algorithms with ciphers, binomial coefficients
and Pascal's triangle, graph traversals, and probability ad expectation.
In the papers (4) and (5), see also the book (3), the author developed a number of integral identities for general sums involving reciprocals of binomial coefficients
where the coefficients 1, 2, 1 are binomial coefficients