KöMaL 2020 B5090

The inscription on one side of a fair coin is $+1$, and $-1$ is on the other side. The coin is tossed $n$ times in a row, and the $n$ results are written down in a row. Then the product of every pair of consecutive items is written below them, resulting in a new list of numbers that only consists of $(n-1)$ items. The procedure is repeated until a single number remains. What is the expected value of the sum of the $\frac{n(n+1)}{2}$ numbers written down in the resulting triangular arrangement of numbers?