Limit distribution of the degrees in scaled attachment random recursive trees

We study the limiting distribution of the degree of a given node‎ ‎in a scaled attachment random recursive tree‎, ‎a generalized random‎ ‎recursive tree‎, ‎which is introduced by Devroye et‎. ‎al (2011)‎. ‎In a‎ ‎scaled attachment random recursive tree‎, ‎every node $i$ is‎ ‎attached to the node labeled $\lfloor iX_i\rfloor$ where $X_0$‎, ‎$\ldots$‎ , ‎$X_n$ is a sequence of i.i.d‎. ‎random variables‎, ‎with‎ ‎support in [0‎, ‎1) and distribution function $F$‎. ‎By imposing a‎ ‎condition on $F$‎, ‎we show that the degree of a given node is‎ ‎asymptotically normal‎.