Evaluate $S_n(n)$ for $S_r(n)=\sum_{m=0}^n(-1)^m m^r\binom{n}{m}$
37650
Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$
87589
Evaluate $\binom{n}{0}+\binom{n}{2}+\binom{n}{4}+...+\binom{n}{2k}$
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
30672
Show that $\sum\limits_{k=0}^n\binom{2n}{2k}^{\!2}-\sum\limits_{k=0}^{n-1}\binom{2n}{2k+1}^{\!2}=(-1)^n\binom{2n}{n}$
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
46840
How to prove that $\sum_{r=0}^n\binom{n}{r}2^r=3^n$
19581
$\sum_{k=0}^n (-1)^k \binom{n}{k}^2$ and $\sum_{k=0}^n k \binom{n}{k}^2$
96945
General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$.
17638
Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
112374
Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$
5049
Proving $\sum_{k=0}^n(-1)^k\binom nk=0$
88124
$M,N\in \Bbb R ^{n\times n}$, show that $e^{(M+N)} = e^{M}e^N$ given $MN=NM$
18046
Prove the following equality: $\sum_{k=0}^n\binom {n-k }{k} = F_n$
8806
Summation of binomial coefficients
48200
Simplify $\sum_{i=0}^n (i+1)\binom ni$
126888
How can you show that $\binom {n}{7}=\sum_{k=7}^n \binom {k-1} {6}$?
110441
Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?