By writing [mathematical expression not reproducible] using a well-known identity of
binomial coefficients and then applying (4), we obtain
Beginning with the negative
binomial coefficients, we again find that greater cultural distance and existing immigrant stocks have negative and positive effects, respectively, on the level of the predicted immigrant stock.
1) is replaced here by the central
binomial coefficient [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Equations (2)-(8) involve
binomial coefficients, whose values are large integer numbers for high upper indices, whereas powers of Courant numbers may be very small real numbers.
In this section we provide a formal definition of the two circulant determinant sequences with
binomial coefficients and derive the formula for their respective n-th term.
n] (I) is a partial sum of signed
binomial coefficients from the n-th row of the Pascal triangle (starting to count from n = 0).
one immediately sees that each
binomial coefficient of the form ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) is even, and if a and are even, then
For the sake of completeness we give, without proof, two particular theorems in regard to single
binomial coefficients and their integral representations.
where the coefficients 1, 2, 1 are
binomial coefficients C(N, x).
Table 1 Regression and Negative
Binomial Coefficients for Bill Introduction in Four Regulatory Agencies, 1949-96 Bills (FGLS) Bills (Negbin) Independent Variables ([dagger]) ([double dagger]) Salience in noncomplex agencies [t.
In order to gain a sense of the magnitude of these effects, the negative
binomial coefficients can be transformed into incidence rate ratios.
Szalay studied the balancing
binomial coefficients, namely, the Diophantine equation
