Let's say we have a sequence T(n) $T(n)$ with the corresponding generating function
A(t)
$$A(t) = \sum \sb {n sum_{n = 0} ^ \infty 0}^\infty T(n) t^n
(sorry it won't let me save an edit with image with it) t^n$$
Is there some relationship between the two functions A(t) $A(t)$ and A(t^2)? $A(t^2)$? And for that matter is there some generalization for any integer power or t?
edit--$t$?
Edit: I'm actually trying to solve for the generating function A(t) $A(t)$ in the equation
A(t)
$$A(t) + (1+t)A(t^2) = t/(1-t^2)t/(1-t^2)$$
this is what inspired my question. My intuition suggested to me that I should look for some kind of relationship between A(t^2) $A(t^2)$ and A(t), $A(t)$, hence the vagueness of my question.
