I have this simple expression:
$$\left(\begin{array}{l} 1\\ +(A)\\ +(A+B)\\ +(A+B+C)\\ +(A+B+C+D)\\ +(A+B+C+D+E)\\ +(A+B+C+D+E+F)\\ +(A+B+C+D+E+F+G)\\ +(A+B+C+D+E+F+G+H)\\ +(A+B+C+D+E+F+G+H) \end{array}\right) \cdot 2^{16}$$
Is there a shorter way to write expressions which have clear patterns?
I'm not sure if this is what you're looking for, but if we let $a_0=A, a_1=B,...,$ then we can express the $n$th term, which we'll call $x_n$, of the sequence $A,A+(A+B),A+(A+B)+(A+B+C),...,$ as $$x_n=\sum_{i=0}^{n-1}(n-i)a_i$$ so if you want the $n$th term, which we'll call $S_n$, of the sequence $1\times 2^{16},(1+A)2^{16},(1+A+(A+B))2^{16},...,$ then set $x_0=0$, and then we can write $$S_n=(1+x_{n-1})2^{16}$$