First, I'm new to Mathematica. I spent my undergraduate programming with Maple, and my computer crashed and I lost it. Fortunately, my university offers free Mathematica downloads to students, so here I am. Is there a best online source for the basics for defining functions, writing programs, etc for a novice Mathematica user?
Now, the meat and potatoes. I am investigating associated Stirling numbers of the second kind (which counts the number of ways to partition $n$ objects into exactly $j$ subsets with at least $t+1$ elements), and I want to look into generating functions for these numbers. I have seen the reference page on combinatorial functions in Mathematica which includes the Stirling numbers, Bell polynomials, etc. Does there exist a function not mentioned here that can generate these associated Stirling numbers, and if not, what is the best way to define this particular function?