# Binomial Coefficients

### Some articles on binomial coefficients, coefficients, coefficient, binomial coefficient:

Binomial Coefficient - Generalizations - Generalization To Multinomials
... Binomial coefficients can be generalized to multinomial coefficients ... They are defined to be the number where While the binomial coefficients represent the coefficients of (x+y)n, the multinomial coefficients represent the coefficients of the polynomial ... The case r = 2 gives binomial coefficients The combinatorial interpretation of multinomial coefficients is distribution of n distinguishable elements over r (distinguishable) containers, each containing ...
Generalizations - Identity For The Product of Binomial Coefficients
... One can express the product of binomial coefficients as a linear combination of binomial coefficients where the connection coefficients are multinomial coefficients ... In terms of labelled combinatorial objects, the connection coefficients represent the number of ways to assign m+n-k labels to a pair of labelled combinatorial objectsâ€”of ... first object, and the unglued part of the second object.) In this regard, binomial coefficients are to exponential generating series what falling ...
Examples Of Generating Functions - Worked Example A: Basics - Bivariate Generating Functions
... For instance, since is the generating function for binomial coefficients for a fixed n, one may ask for a bivariate generating function that generates the ... find the generating function in y that has these as coefficients ... function for is just, the generating function for the binomial coefficients is and the coefficient on is the binomial coefficient ...