Let-n-be-a-positive-integer-Prove-that-k-0-n-2-k-n-k-n-k-n-k-2-2n-1-n-

Question Number 120188 by benjo_mathlover last updated on 30/Oct/20

L e t n b e a p o s i t i v e i n t e g e r .

P r o v e t h a t \underset{k = 0}{\sum^{n}} 2^{k} (\begin{matrix} n \\ k \end{matrix}) (\begin{matrix} n - k \\ ⌊ \frac{n - k}{2} ⌋ \end{matrix}) = (\begin{matrix} 2 n + 1 \\ n \end{matrix})