Binomial coefficients with sums $\sum_{i=0}^ni^2{n\choose i} $
127150
Finding general formula of $\sum_{i=0}^n i^2 \binom{n}{i}$
70248
Closed-form expression for $\sum_{k=0}^n\binom{n}kk^p$ for integers $n,\,p$
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
25826
Proof of a combinatorial identity: $\sum\limits_{i=0}^n {2i \choose i}{2(n-i)\choose n-i} = 4^n$
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
90904
Combinatorial proof of an identity with squared binomial coefficients
143927
Binomial coefficients that are powers of 2
115686
A finite summation of double binomial coefficients
147910
Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$
146762
Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
16347
Induction: $\sum_{k=0}^n \binom nk k^2 = n(1+n)2^{n-2}$
109599
A finite sum involving the binomial coefficients and the harmonic numbers
47670
Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$
115236
Calculate the sum of inverse values of ${n\choose 0}, {n\choose 1}, ... {n\choose n}$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
49234
Sum of binomial coefficients with index divisible by 4
76828
Evaluating $\sum_{i = 0}^{\lfloor n/2 \rfloor} {n \choose 2i}p^{2i}(1 - p)^{n - 2i}$