VTRMC 1980 Problem 2

The sum of the first $n$ terms of the sequence $$1,1+2,1+2+2^2,\ldots,1+2+\cdots+2^{k-1},\ldots$$ is of the form $2^{n+R}+Sn^2+Tn+U$ for all $n>0.$ Find $R,S,T,$ and $U.$