Newbetuts

About an inequality with central binomial coefficients ${2N \choose N }<2^N {N \choose N/2 }<2 {2N \choose N }$.

How to algebraically prove $\binom{n+m}{2} = nm + \binom{n}{2} + \binom{m}{2}$?

Limit of sum with binomial coeffs

Counting subsets with r mod 5 elements

Determinants of products of binary matrices and binomial coefficients

Proof of $\sum_{m=0}^{n}\binom{m}{j}\binom{n-m}{k-j}=\binom{n+1}{k+1}$ (Another form of the Chu–Vandermonde identity)

An asymptotic expression of sum of powers of binomial coefficients.

Computing $\sum\limits_{r=1}^{n} r^{4}\binom{n}{r}^{2}$

How was the integral formula for the binomial coefficient discovered?

Evaluating the expression: $\sum\limits_1^n(-1)^{k-1}\frac{n \choose k}{k^2}$

Bonferroni Inequalities

Closed form for a sum involving binomial coefficients

How to simpify the following equation involving binomial coefficients?

Prove $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^n = n!$ and $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^m = 0$

Problem of limit with binomial coefficients

Binomial limit $\left(\binom{3n}{n}\binom{2n}{n}^{-1}\right)^{1/n}$ as $n\to \infty$

New posts in binomial-coefficients

Challenge: How to prove this identity between bi- and trinomial coefficients?

Determinant of a Pascal Matrix, sort of

Factorial canceling on expansion of binomial coefficients on Concrete Mathematics

Binomial coefficients: how to prove an inequality on the $p$-adic valuation?

About an inequality with central binomial coefficients ${2N \choose N }<2^N {N \choose N/2 }<2 {2N \choose N }$.

How to algebraically prove $\binom{n+m}{2} = nm + \binom{n}{2} + \binom{m}{2}$?

Limit of sum with binomial coeffs

Counting subsets with r mod 5 elements

Determinants of products of binary matrices and binomial coefficients

Proof of $\sum_{m=0}^{n}\binom{m}{j}\binom{n-m}{k-j}=\binom{n+1}{k+1}$ (Another form of the Chu–Vandermonde identity)

An asymptotic expression of sum of powers of binomial coefficients.

Computing $\sum\limits_{r=1}^{n} r^{4}\binom{n}{r}^{2}$

How was the integral formula for the binomial coefficient discovered?

Evaluating the expression: $\sum\limits_1^n(-1)^{k-1}\frac{n \choose k}{k^2}$

Bonferroni Inequalities

Closed form for a sum involving binomial coefficients

How to simpify the following equation involving binomial coefficients?

Prove $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^n = n!$ and $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^m = 0$

Problem of limit with binomial coefficients

Binomial limit $\left(\binom{3n}{n}\binom{2n}{n}^{-1}\right)^{1/n}$ as $n\to \infty$