What is the sum $\sum_{k=0}^{n}k^2\binom{n}{k}$?
30338
How to prove that $\sum_{k=0}^n \binom nk k^2=2^{n-2}(n^2+n)$
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
16347
Induction: $\sum_{k=0}^n \binom nk k^2 = n(1+n)2^{n-2}$
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
14239
How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$
44111
Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?
112253
How to find sums like $\sum_{k=0}^{39} \binom{200}{5k}$
136580
Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$
127150
Finding general formula of $\sum_{i=0}^n i^2 \binom{n}{i}$
5332
Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$
94060
Sum of square binomial coefficients
106552
Find the sum of $\sum \frac{1}{k^2 - a^2}$ when $0<a<1$
5049
Proving $\sum_{k=0}^n(-1)^k\binom nk=0$
18046
Prove the following equality: $\sum_{k=0}^n\binom {n-k }{k} = F_n$
87589
Evaluate $\binom{n}{0}+\binom{n}{2}+\binom{n}{4}+...+\binom{n}{2k}$
147910
Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$