Closed form for series $\sum_{m=1}^{N}m^n\binom{N}{m}$
114911
Evaluate $\sum_{k = 0}^{n} {n\choose k} k^m$
23726
A closed form for $1^{2}-2^{2}+3^{2}-4^{2}+ \cdots + (-1)^{n-1}n^{2}$
151085
Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$
107433
Prove the sum to n terms of the series
108401
Sum of binomial coefficients $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{2n - 2k}{n - 1} = 0$
116722
Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$
139307
Closed form expression for infinite series
5537
Closed form for $ \int_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$
158774
Series of binomial coefficients: $\sum\limits_{n=k}^{\infty}{\binom nk}x^n=\frac{x^k}{(1-x)^{k+1}}$
140462
Find a closed form for the power series $f_p(x)=\sum\limits_{n=0}^\infty\frac{n^p}{n!}x^n$
35342
Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
117863
Series $\sum_{n=1}^\infty \frac{n^n}{(n!)^2}$
39199
closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$
38760
Infinite Series $\sum\limits_{n=0}^\infty\frac{(-1)^n}{(2n+1)^{2m+1}}$
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
109576
Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$
152802
How find series $\sum_{n=1}^{\infty}\frac{(-1)^{[\sqrt[m]{n}]}}{n^a}$?