Newbetuts

combinatorics - take all the balls out of a basket so that number of the balls from each color be always unequal.

Finding the sum $\sum_{k=1}^rk^2\binom {n-k}{r-k}$

Staver's identity relating $\sum_{k=1}^{n}\binom{2k}{k}\frac{1}{k}$ and $\sum_{k=1}^{n}\left(k\binom{n}{k}\right)^{-2}$

Prove the roots of these exponential functions are integers?

Alternative Notation for Binomial Coefficient

Inequality with binomial coefficients $ \binom{2n-1}{n} + \binom{2n-1}{n+1} + \cdots + \binom{2n-1}{n+z} \geq (2z+3)\binom{2n-2}{n+z} $

Divisibility of binomial coefficient by prime power - Kummer's theorem

Smoothstep sigmoid-like function: Can anyone prove this relation?

Combinatorial proof that $\sum_{k=0}^n \binom{n}{k} \frac{(-1)^k}{(k+1)^2} = \frac{H_{n+1}}{n+1}$

Let $a_k=\frac1{\binom{n}k}$, $b_k=2^{k-n}$. Compute $\sum_{k=1}^n\frac{a_k-b_k}k$

How to simplify this combinatorial sum

proof that $1 = \sum\limits_{k=0}^n (-1)^k { 2n \choose n,k,n-k } \frac{n}{n+k}$

Obtaining binomial coefficients without "counting subsets" argument

Which is better way to calculate nCr

A sum with binomial coefficients

A limit on binomial coefficients

New posts in binomial-coefficients

Reciprocal binomial coefficient polynomial evaluation

Prove the lecturer is a liar...

Bijection for $q$-binomial coefficient

Prove $\sum_{i=0}^n \binom{n}{i}^2x^{n-i} = 0$ has $n$ negative roots

combinatorics - take all the balls out of a basket so that number of the balls from each color be always unequal.

Finding the sum $\sum_{k=1}^rk^2\binom {n-k}{r-k}$

Staver's identity relating $\sum_{k=1}^{n}\binom{2k}{k}\frac{1}{k}$ and $\sum_{k=1}^{n}\left(k\binom{n}{k}\right)^{-2}$

Prove the roots of these exponential functions are integers?

Alternative Notation for Binomial Coefficient

Inequality with binomial coefficients $ \binom{2n-1}{n} + \binom{2n-1}{n+1} + \cdots + \binom{2n-1}{n+z} \geq (2z+3)\binom{2n-2}{n+z} $

Divisibility of binomial coefficient by prime power - Kummer's theorem

Smoothstep sigmoid-like function: Can anyone prove this relation?

Combinatorial proof that $\sum_{k=0}^n \binom{n}{k} \frac{(-1)^k}{(k+1)^2} = \frac{H_{n+1}}{n+1}$

Let $a_k=\frac1{\binom{n}k}$, $b_k=2^{k-n}$. Compute $\sum_{k=1}^n\frac{a_k-b_k}k$

How to simplify this combinatorial sum

proof that $1 = \sum\limits_{k=0}^n (-1)^k { 2n \choose n,k,n-k } \frac{n}{n+k}$

Obtaining binomial coefficients without "counting subsets" argument

Which is better way to calculate nCr

A sum with binomial coefficients

A limit on binomial coefficients