Just Sum It

Given the number of available digits from $1$ to $9$, sum all possible numbers generated from those digits. For example,

Digit $2$ can be used twice when forming a number, while digits $4$ and $6$ can be used once each. There are exactly $34$ distinct numbers that can be constructed using the above digits: $2$, $4$, $6$, $22$, $24$, $26$, $42$, $46$, $62$, $64$, $224$, $226$, $242$, $246$, $262$, $264$, $422$, $426$, $462$, $622$, $624$, $642$, $2246$, $2264$, $2426$, $2462$, $2624$, $2642$, $4226$, $4262$, $4622$, $6224$, $6242$, $6422$. The sum of all those numbers is $51622$.