Sum of binomial numbers alternating the sign.
133076
Prove this sum equal to an expression.
122891
integer as sum of three binomials
101011
An intriguing relation between two alternating series
113321
Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$
51008
Evaluating a sum involving binomial coefficient in denominator
83229
Nested summations and their relation to binomial coefficients
75910
Combinatorial Proof of Combinatorial Identity involving $(-1)^k \binom {n-1}{k}$
32260
Alternating Sum of Cubes
20713
The sum of an uncountable number of positive numbers
48200
Simplify $\sum_{i=0}^n (i+1)\binom ni$
101573
Subtracting even and odd binomial coefficients?
39199
closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$
56828
A combinatorial proof that the alternating sum of binomial coefficients is zero
60965
Representing a nonnegative integer as the ordered sum of odd numbers
65335
A "binomial" generalization of harmonic numbers
94060
Sum of square binomial coefficients
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$