New posts in Binomial Coefficients

Is there a closed form for $\sum_{n=1}^\infty\frac{2^{2n}H_n}{n^3{2n\choose n}}?$

Computing $\sum_{n=1}^\infty\frac{2^{2n}H_{n+1}}{(n+1)^2{2n\choose n}}$

Intuition behind sums of sums of whole numbers

Show $\binom{n}{[n/2]} = \binom{n-1}{[(n-1)/2]} + \sum_{i=0}^{[n/2] - 1} \frac{1}{i+1} \binom{2i}{i} \binom{n-2i-2}{[n/2]- i - 1}$

$n$ is prime iff $\binom{n^2}{n} \equiv n \pmod{n^4}$?

Is the summation $\sum_{i=1}^{n}\frac1{i} \binom{n}{i}$ possible?

Is there a story proof behind the combinatorial identity $(n-2k)\binom{n}{k} = n\left[ \binom{n-1}{k} - \binom{n-1}{k-1} \right]$?

No. of positive integral solutions and link to coefficients in expansion

Bound for $\sum_{k=0}^{n}(-1)^k{3n\choose k}{n\choose k}$.

A summation similar to Vandermonde identity