What is the Result of this Factorial Identity?
17638
Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
50226
Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$
139411
Finding $\pi$ factorial
65983
Combinatorial proof of binomial coefficient summation identity
145900
Proof of a double summation reduction identity
128913
A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$
48881
Verification the integral identity $\int_0^\pi \ln(1+\alpha\cos(x))dx=\pi\ln\left(\frac{1+\sqrt{1-\alpha^2}}{2}\right)$.
33104
Combinatorial Proof with Summation Identity
56138
Proving $\sum_{k=0}^{2m}(-1)^k{\binom{2m}{k}}^3=(-1)^m\binom{2m}{m}\binom{3m}{m}$ (Dixon's identity)
96961
A proof for the identity $\sum_{n=r}^{\infty} {n \choose r}^{-1} = \frac{r}{r-1}$
10777
Proof of the identity $2^n = \sum\limits_{k=0}^n 2^{-k} \binom{n+k}{k}$
63314
Triangular Factorials
83981
How to prove those "curious identities"?
48446
Summation involving a factorial: $1 + \sum_{j=1}^{n} j!j$
142882
Can the factorial function be written as a sum?
78314
Generating function for the factorial sequence
15666
explanation for a combinatorial identity involving the binomial coefficient