  We report electronic structure calculations for BaTi$_2$Sb$_2$O and discuss
the results in relation to the observed superconductivity of this material when
hole doped with Na. The Fermi surface shows several sheets. These include a
nested nearly 2D cylinder. There are also two sheets, which are three
dimensional, in spite of the layered crystal structure. A magnetic instability
associated with Fermi surface nesting is found. A sign-changing s-wave state,
different from the one in the Fe-based superconductors, is predicted within a
scenario of spin-fluctuation mediated superconductivity.
