binomial coefficient

In particular, E are the binomial coefficients of power 1 α.

This is a real vector space of dimension binomial coefficient.

These turn out to be the binomial coefficients.

Binomial coefficients count subsets of prescribed size from a given set.

Binomial coefficients can be computed explicitly in various ways.

(2) The formula for the binomial coefficient is usually expressed as: n!

He managed to approximate the binomial coefficients and factorial.

To get from the fourth to fifth line manipulations using the generalized binomial coefficient is needed.

In mathematics, Pascal's rule is a combinatorial identity about binomial coefficients.

The tetrahedral numbers can also be represented as binomial coefficients:

Thus many identities on binomial coefficients carry over to the falling and rising factorials.

This formula is easiest to understand for the combinatorial interpretation of binomial coefficients.

The Narayana numbers can be expressed in terms of binomial coefficients:

In general, the number of m-faces is equal to the binomial coefficient .

Many series involving the binomial coefficient may be derived:

Many relations for the Stirling numbers shadow similar relations on the binomial coefficients.

Note that, although this formula involves a fraction, the binomial coefficient is actually an integer.

The binomial coefficient can be interpreted as the number of ways to choose k elements from an n-element set.

This is made possible by a careful analysis of the prime factorization of central binomial coefficients.

Then after the following property of binomial coefficient:

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.

Problems that admit combinatorial proofs are not limited to binomial coefficient identities.

The rising and falling factorials can be used to express a binomial coefficient:

The definition of the binomial coefficients can be extended to the case where is real and is integer.

Here, is the binomial coefficient and and .