Evaluating $\sum^{n-1}_{j=0} \binom{n}{j}\binom{n}{j+1}$
75367
Find a simple formula for $\binom{n}{0}\binom{n}{1}+\binom{n}{1}\binom{n}{2}+...+\binom{n}{n-1}\binom{n}{n}$
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
39909
Getting a closed form from $\sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \sum_{k=1}^{j} 1$
116461
Prove the identity $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}=0$ using a combinatorial interpretation of the positive and negative terms
74294
How to simplify $\sum_{i=1}^{k}\binom{n + i - 1}{i}$?
87479
Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
28027
Find $\sum_{k=0}^{n}4^k \binom{n}{k}$
5049
Proving $\sum_{k=0}^n(-1)^k\binom nk=0$
39199
closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$
44111
Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
6416
How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
125148
Summation of series $\sum_{k=0}^\infty 2^k/\binom{2k+1}{k}$
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
116722
Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$
83229
Nested summations and their relation to binomial coefficients