  In the type-I seesaw model the size of mixing between light and heavy
neutrinos, nu and N, respectively, is of order the square root of their mass
ratio, (m_nu/m_N)^(1/2), with only one generation of the neutrinos. Since the
light-neutrino mass must be less than an eV or so, the mixing would be very
small, even for a heavy-neutrino mass of order a few hundred GeV. This would
make it unlikely to test the model directly at the LHC, as the amplitude for
producing the heavy neutrino is proportional to the mixing size. However, it
has been realized for some time that, with more than one generation of light
and heavy neutrinos, the mixing can be significantly larger in certain
situations. In this paper we explore this possibility further and consider
specific examples in detail in the context of type-I seesaw. We study its
implications for the single production of the heavy neutrinos at the LHC via
the main channel q qbar' -> W^* -> l N involving an ordinary charged lepton l.
We then extend the discussion to the type-III seesaw model, which has richer
phenomenology due to presence of the charged partners of the heavy neutrinos,
and examine the implications for the single production of these heavy leptons
at the LHC. In the latter model the new kinds of solutions that we find also
make it possible to have sizable flavor-changing neutral-current effects in
processes involving ordinary charged leptons.
