Δx(k + xf) = k2 + xΔx(f)
(assuming f is a formal power series over x) then I could express the generating function for the number of AVL trees of height n by (omitting all the subscript xs for brevity)
f = x(Δf + Δ((1+x)f) + Δ((1-x)f))
It's also too bad Δ doesn't seem to be linear or homomorphic on products or anything else nice like that.
