Evaluating the sum of $\sum_{k=0}^n \binom{n}{k}^2$
6366
Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$
122024
Asymptotic of a sum involving binomial coefficients
132984
$\sum\limits_{k=0}^{\frac{p-1}2}3^k\binom{p}{k}\equiv 2^p-1\pmod{p^2}$
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
99843
How to simplify $ \sum_{k=0}^{\infty} \binom{k + r - 1}{k} x^k$
112374
Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$
146762
Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
147910
Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$
54604
Evaluate $ \sum_{m > n > 0} \frac{m^2 - n^2}{(m^2 + n^2)^2} $
51008
Evaluating a sum involving binomial coefficient in denominator
87589
Evaluate $\binom{n}{0}+\binom{n}{2}+\binom{n}{4}+...+\binom{n}{2k}$
125148
Summation of series $\sum_{k=0}^\infty 2^k/\binom{2k+1}{k}$
115433
Find the summation of given expression: $\sum_{k=1}^n k^3\binom nk$
37007
Evaluating $\sum_{k=1}^{n} \frac{1}{k(k+1)}$
113321
Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$
131326
How to find $\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}$?
112827
Find the sum of the binomial coefficients