For a simply connected space X of finite type and a prime p, let \(R_{\pi}\) and \(R_ H\) indicate the radii of convergence of the two power series \(P_{\pi}(X)=\sum (\dim \pi_ n(X)\otimes Z_ p)\cdot t^ n\) and \(P_ H(X)=\sum (\dim H_ n(\Omega X;Z_ p))\cdot t^ n,\) respectively. The author gives a partial answer to the Henn conjecture [H.-W. Henn, Manuscr. Math. 56, 235-245 (1985; Zbl 0605.55009)]. Namely, \(\min \{1,R_{\pi}\}\leq R_ H\) for all simply connected spaces of finite type.