Is there a way to simplify this expression including summation, powers of 2 and binomial coefficients
116491
Closed form for $\sum_{k=0}^{m} {\binom {m}{k}} a^{k} (b+ck)^N$
124229
Simplify $\sum_{k=0}^{\infty} x^ky^{\frac{k(k+1)}{2}}$
65648
Different ways to come up with $1+2+3+\cdots +n=\frac{n(n+1)}{2}$
125712
Working with binomial coefficient $\sum_{k=0}^n (-1)^k \binom nk=0$
146810
How to derive this binomial identity?
6803
Expression for power of a natural number in terms of binomial coefficients
142994
How to show $\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$?
151757
Simplify $\sum_{i=0}^{N/2}{N-i\choose i}$
97984
Express as sum of powers
78632
Summation equation for $2^{x-1}$
112827
Find the sum of the binomial coefficients
87589
Evaluate $\binom{n}{0}+\binom{n}{2}+\binom{n}{4}+...+\binom{n}{2k}$
151085
Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$
65983
Combinatorial proof of binomial coefficient summation identity
87505
binomial coefficient equal to sum
51008
Evaluating a sum involving binomial coefficient in denominator
39199
closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$