  Triply heavy baryons are very interesting hadrons to be explored for they
provide particular information about strong interactions, hadron structures,
and weak decays of heavy baryons. We calculate the hadronic production cross
sections of the \Omega_{ccc} and the \Omega_{ccb}, which are dominated by the
gg fusion subprocesses containing 4362 and 1454 Feynman diagrams, respectively.
A method for generating and calculating tree level Feynman diagrams
automatically is developed to deal with complicated processes containing so
many diagrams. Our results show that 10^4-10^5 events of triply heavy baryons
can be accumulated for 10 fb^{-1} integrated luminosity at LHC. Signatures of
the triply heavy baryons are pointed out, with emphasis on the decay modes
\Omega_{ccc} -> \Omega_{sss} + 3 \pi^+ and \Omega_{ccb} -> \Omega_{sss} + 3
\pi^+ +\pi^-. We conclude that it is quite promising to discover them at LHC.
