Does this sum involving the central binomial coefficient have a closed form expression?
96945
General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$.
105237
Alternating sum of binomial coefficients identity
134361
Calculating the sum of a binomial coefficient series
58972
Proof/Derivation of Closed form of Binomial Expression $\sum\limits_{k=0}^{2n}(-1)^k\binom{2n}{k}^2$
122024
Asymptotic of a sum involving binomial coefficients
110441
Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?
125148
Summation of series $\sum_{k=0}^\infty 2^k/\binom{2k+1}{k}$
39659
Is there a closed formula for this summation?
142882
Can the factorial function be written as a sum?
35381
Sum with binomial coefficients: $\sum_{k=1}^m  \frac{1}{k}{m \choose k} $
46132
Combinatorial interpretation for the identity $\sum\limits_i\binom{m}{i}\binom{n}{j-i}=\binom{m+n}{j}$?
79814
Calculate sums of inverses of binomial coefficients
47753
Closed form of series with factorial-squared denominator?
14399
Calculate $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k}$
91458
Sum of the series $\binom{n}{0}-\binom{n-1}{1}+\binom{n-2}{2}-\binom{n-3}{3}+..........$
59252
Show $\sum_{k=0}^{m} \binom{n-k}{m-k}=\binom{n+1}{m}$
133420
Computing the binomial series: $\binom{n}{2}\cdot2^2+\binom{n}{4}\cdot2^4+\binom{n}{6}\cdot2^6+\cdots+ \binom{n}{n}\cdot2^n$