  The dynamical structure factor of the Babujan-Takhtajan antiferromagnetic
spin-1 chain is computed numerically at zero temperature and zero magnetic
field, using the higher-spin generalization of an Algebraic Bethe Ansatz-based
method previously used for spin-1/2 integrable chains. This method, which
consists in the explicit construction of eigenstates and the summation of the
Lehmann representation of the correlator, is here particularly challenging to
implement in view of the presence of strongly deviated string solutions to the
Bethe equations. We show that a careful treatment of these deviations makes it
possible to obtain perfect saturation of sum rules for small system sizes, and
extremely good saturation for large system sizes where the dynamical structure
factor is computed by including all two-spinon and four-spinon contributions.
The real-space spin-spin correlation, obtained by Fourier transforming our
results, displays asymptotics fitting predictions from conformal field theory.
