Tessellate S.T.E.M.S. (2019) - Mathematics - Category A (School) - Set 4 -Objective Problem 1

Find a closed form for the following sum

$\binom{2019}{0} \binom{0}{0} 2^{2019} + \binom{2019}{1}\binom{1}{0} 2^{2018} + \binom{2019}{2}\binom{2}{1} 2^{2017} + \binom{2019}{3}\binom{3}{1} 2^{2016} + \cdots + \binom{2019}{2018} \binom{2018}{1009} 2 + \binom{2019}{2019} \binom{2019}{1009}$

This problem is a part of Tessellate S.T.E.M.S. (2019)