Laplace II: Steps, Impulses & Convolution · Superchallenge problem

Let $f(t)=te^{-t}$ and let $f^{*n}$ denote $f*f*\cdots*f$ ($n$ factors). The series $R(t)=\displaystyle\sum_{n=1}^{\infty}f^{*n}(t)$ converges for all $t\ge0$. Find $R(\ln 2)$.