Sum of product of binomial coefficients.
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
42606
Orthogonality for Binomial Coefficients
142303
Alternating sum of binomial coefficients multiplied by (1/k+1)
94784
$\sum_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$ using Counting argument
74294
How to simplify $\sum_{i=1}^{k}\binom{n + i - 1}{i}$?
31970
Alternating sum of squares of binomial coefficients
86194
Infinite series with the binomial coefficient
148949
Find the value of $\sum_{k=1}^{n} k \binom {n} {k}$
131326
How to find $\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}$?
35381
Sum with binomial coefficients: $\sum_{k=1}^m  \frac{1}{k}{m \choose k} $
91239
Sum of binomial coefficients involving $n,p,q,r$
44621
Simple binomial theorem proof: $\sum_{j=0}^{k} \binom{a+j}j = \binom{a+k+1}k$
17551
Truncated alternating binomial sum
83229
Nested summations and their relation to binomial coefficients
108688
An identity involving products of sums
91458
Sum of the series $\binom{n}{0}-\binom{n-1}{1}+\binom{n-2}{2}-\binom{n-3}{3}+..........$
5332
Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$