RetinaRetina 0.8.2, 13 bytes
.+
$*
1
$`1
1
Try it online! Explanation: The first and last stages are just unary ⇔ decimal conversion. The middle stage replaces each 1
with the number of 1
s to its left plus another 1
for the 1
itself, thus counting from 1
to n
, summing the values implicitly.