  We examine the rationality conjecture which states that (a) the formal power
series $\sum_{r\ge 1} \tc_{r+1}(X)\cdot x^r$ represents a rational function of
$x$ with a single pole of order 2 at $x=1$ and (b) the leading coefficient of
the pole equals $\cat(X)$. Here $X$ is a finite CW-complex and for $r\ge 2$ the
symbol $\tc_r(X)$ denotes its $r$-th sequential topological complexity. We
analyse an example (violating the Ganea conjecture) and conclude that part (b)
of the rationality conjecture is false in general. Besides, we establish a
cohomological version of the rationality conjecture.
