I want to solve $$T(n)=3T\bigl(\bigl\lfloor \frac{n}{3}\bigr\rfloor\bigr) +2n\log n,$$ with base case $T(n) = 1$ if $n \leq 1$.
I am sure that the Master Theorem does not work. I am trying a lot with the substitution method, but I am very frustrated since I can't find a solid expression. Does any one have a good "hint" or good idea on how to solve this in a nice way?