hxthanh
- 15
- 0
Evaluate sum:
$\displaystyle S=\sum_{k=0}^{2n}(-1)^k{2n\choose k}{4n\choose 2k}$
$\displaystyle S=\sum_{k=0}^{2n}(-1)^k{2n\choose k}{4n\choose 2k}$
I believe that the answer must be $$S = \frac{(-1)^n(6n)!(2n)!}{(4n)!(3n)!n!}$$, but I have NO idea how one might prove that.hxthanh said:Evaluate sum:
$\displaystyle S_n=\sum_{k=0}^{2n}(-1)^k{2n\choose k}{4n\choose 2k}$
Your result is absolute correct!(Clapping)Opalg said:I believe that the answer must be $$S = \frac{(-1)^n(6n)!(2n)!}{(4n)!(3n)!n!}$$, but I have NO idea how one might prove that.
...