Is there a closed form for $(x + D)^n$ where D is the differential operator with respect to x?
Avi's comment in this post helped me understand this expression a bit better, but I'm still curious if you can write it out with sums and binomial coefficients in some clever way.
Edit: I ran into this expression while deriving properties of the Hermite polynomials so I could use them in the context of a harmonic oscillator. This question is purely out of mathematical curiosity.