Series of inverse function $A(s) = \sum_{k>0}a_ks^k$ and $A(s)+A(s)^3=s$.
I want calculate $a_5$. What ways to do it most efficiently?

Another possibility: the Lagrange inversion formula
$A$ is the inverse of $B(t)=t+t^3$, so
$$A(s)=\sum_{n=1}^\infty\lim_{t\to 0}\frac{s^n}{n!}\frac{d^{n-1}}{dt^{n-1}}\left(\frac{t}{t+t^3}\right)^n.$$
