Inverse of series $z+a_2z^2+...$ Let $p$ be a power series with integer coefficients of the special form $p(z)=z+a_2z^2+a_3z^3+..$. I wonder if the inverse (composition not $1/p$) series has again integer coefficients. 
I have calculated some of such series so I guess yes. What do you think?

Yes it is correct, either you assume 
1) the original series converges in some where as a Taylor series; or 
2) just "formal" calculations.
The key is you can list out a series of equations 
b_1a_1=1
b_n + b_{n-1}a_1 + .. = 0 (n>1)
And you can decide one by one b_n. 
