Mean of ten-digit numbers with digits near their place

Write a ten-digit number as $\overline{d_9d_8\ldots d_1d_0}$ (leading digit $d_9\neq0$). Consider all such numbers in which every digit differs from its place index by at most one, i.e. $|d_i-i|\le1$ for $i=0,\dots,9$. What is the average of these numbers?

$18753086421/2=9376543210.5$. The digits are chosen independently and uniformly from their allowed sets: $d_0\in\{0,1\}$, $d_9\in\{8,9\}$, and $d_i\in\{i-1,i,i+1\}$ otherwise, with means $0.5$, $8.5$ and $i$. By linearity the average is $9376543210$ (the middle digits at their means, units $0$, leading $9$) shifted by $-10^9/2+1/2$, i.e. $9376543210.5$.