Closed form for $S= \sum\limits_{k=0}^n x^k \binom{n}{k}^2$
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
128608
Closed form for the series $a+a^p+(a^p)^p+\dots$
69084
What is the closed form for $\sum_{n=1}^\infty \frac1n - \frac1{n+1/p}$?
83346
Finding a closed form $x_n$ for the recurrence relation $x_{n+2} = px_{n+1} + qx_n + r$
146651
Evaluting sum $\sum \limits_{n=0}^\infty\frac{n^k}{n!}$
1167
How to prove that $\sum_{k=0}^{n}(-1)^k \binom {n}{k}=0 $
48200
Simplify $\sum_{i=0}^n (i+1)\binom ni$
6366
Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$
118571
Why is $\sum\limits_{k=0}^{n}(-1)^k\binom{n}{k}^2=(-1)^{n/2}\binom{n}{n/2}$ if $n$ is even?
99843
How to simplify $ \sum_{k=0}^{\infty} \binom{k + r - 1}{k} x^k$
47753
Closed form of series with factorial-squared denominator?
92754
Closed form for the series: $\sum_{n=1}^{\infty}x^{n^2}$
118436
Identifying the series $\sum\limits_{k=-\infty}^{\infty} 2^k x^{2^k}$
116491
Closed form for $\sum_{k=0}^{m} {\binom {m}{k}} a^{k} (b+ck)^N$
5332
Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$
49771
Prove that $\sum\limits_{k=0}^r\binom{n+k}k=\binom{n+r+1}r$ using combinatoric arguments.
121617
Closed form of $\sum_{n=0}^{\infty} \frac{\cos(\alpha \, n)}{n!}$