I've the following formula (taken from Hong Qian - Fractional Brownian Motion and Fractional Gaussian Noise):
$$ \sum_P \prod_{j=1}^n E[X_j, X_{P_j}] $$
where the sum runs over all permutations P: j → Pj of the positive integers j.
I tried to make an example in the case $n=4$:
$$ \sum_P \prod_{j=1}^4 E[X_j, X_{P_j}] = \sum_P E[X_1, X_{P_1}] E[X_2, X_{P_2}] E[X_3, X_{P_3}] E[X_4, X_{P_4}] $$
Can you tell me how to continue?
EDIT: alternative way to write the above formula (from Wikipedia):
$$ \sum_{p \in P_n^2} \prod_{i, j \in p} E[X_i X_j] $$
where the sum is over all the pairings of $\{1,\ldots,n\}$, i.e. all distinct ways of partitioning $\{1,\ldots,n\}$ into pairs ${\displaystyle \{i,j\}}$, and the product is over the pairs contained in $p$.