If, for example, I have a nesting function like
Nest[1 + x^n (#) &, 1, 3]
it gives the result
1 + x^n (1 + x^n (1 + x^n))
I would need the
n to increase by one with every step, just like in a sum or product function, so that the result would be
1 + x^1 (1 + x^2 (1 + x^3))
Is there a way to do this in Mathematica? If so, how?