Prove:
Start with the binomial theorem:
.....(1)
Differentiate w.r.t. x, then multiply through by x:
....(2)
Take (2) * (2):
Consider the coefficient of in the preceding equation:
Use :
....3
Now it becomes apparent we are going to need to find
, so consider (1) * (2):
.
Extracting the coefficient of ,
so
....(4)
n * (4) - (3) yields
so