How to find the generating function for $a_n = \binom{2n}{n}$?
51509
How to show that $1 \over \sqrt{1 - 4x} $ generates $\sum_{n=0}^\infty \binom{2n}{n}x^n $
148949
Find the value of $\sum_{k=1}^{n} k \binom {n} {k}$
89705
How to solve $a_n = 2a_{n-1} + 1, a_0 = 0, a_1 = 1$?
127150
Finding general formula of $\sum_{i=0}^n i^2 \binom{n}{i}$
70997
showing a genereral function from a generating function and recursive function
75367
Find a simple formula for $\binom{n}{0}\binom{n}{1}+\binom{n}{1}\binom{n}{2}+...+\binom{n}{n-1}\binom{n}{n}$
143337
How to prove that $\sum_{i=0}^n 2^i\binom{2n-i}{n} = 4^n$.
30672
Show that $\sum\limits_{k=0}^n\binom{2n}{2k}^{\!2}-\sum\limits_{k=0}^{n-1}\binom{2n}{2k+1}^{\!2}=(-1)^n\binom{2n}{n}$
116491
Closed form for $\sum_{k=0}^{m} {\binom {m}{k}} a^{k} (b+ck)^N$
35712
Solve for n: $\varphi(2n)=\varphi(3n)$
85786
Generating functions of partition numbers
138456
How to fit $\sum{n^{2}x^{n}}$ into a generating function?
146810
How to derive this binomial identity?
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
36361
How to calculate the summation $(\sum_{p = k}^{n} \binom{n}{p}) / 2^n$ quickly?
136580
Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$
142994
How to show $\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$?