  Spontaneous formation of knots in long polymers at equilibrium is inevitable
but becomes rare in sufficiently short chains. Here, we show that knotting and
knot complexity increase by orders of magnitude in diblock polymers with a
fraction $p$ of self-propelled monomers. Remarkably, this enhancement is not
monotonic in $p$ with an optimal value independent of the monomer's activity.
By monitoring the knot's size and position we elucidate the mechanisms of its
formation, diffusion, and untying and ascribe the non-monotonic behaviour to
the competition between the rate of knot formation and the knot's lifetime.
These findings suggest a non-equilibrium mechanism to generate entangled
filaments at the nano-scale.
