  Using the notion of the composita, we obtain a method of solving iterative
functional equations of the form $A^{2^n}(x)=F(x)$, where $F(x)=\sum_{n>0}
f(n)x^n$, $f(1)\neq 0$. We prove that if $F(x)=\sum_{n>0} f(n)x^n$ has integer
coefficients, then the generating function $A(x)=\sum_{n>0}a(n)x^n$, which is
obtained from the iterative functional equation $4A(A(x))=F(4x)$, has integer
coefficients.
  Key words: iterative functional equation, composition of generating
functions, composita.
