Let the generation function for $A_n$ is the polynomial $\prod_{k=1}^{n}\frac {(1-x^{k+1})} {(1-x)}$ as defined in OEIS.
For eg. for $n=5$ we have numbers: $1, 5, 14, 29, 49, 71, 90, 101, 101, 90, 71, 49, 29, 14, 5, 1$, etc for other $n$.
I wonder how to calculate the mean and the variance of such a distribution for any $n$? Actually I am looking for a clear explanation how to derive the final result. Any help are highly welcomed.