Rearranging the sequence
ES6, 118 81 78 bytes

n=&gt;[...[...Array(n).keys()].join``].map(c=&gt;r/=(o[c]=-~o[c])/i++,o=[],i=r=1)&amp;&amp;r


Someone's bound to tell me there's a shorter way of concatenating the numbers up to n.

Saved a cool 37 bytes by taking @edc65's idea and running it on steroids. (Save an extra byte by using '|' instead of &amp;&amp; but that limits the result to 31 bits.)

Edit: Saved 3 further bytes again thanks to @edc65.