A permutation of integers $1, 2, 3, \ldots, n$ is called hilly if the 2nd, 4th, 6th, $\ldots$ terms are greater than their neighbors. For example, $3,4,1,2$ is hilly while $1,4,3,2$ is not hilly since the fourth term (2) is not greater than the third term (3). Find the number of hilly sequences of length 7.