  Spin and charge fluctuations and superconductivity in a recently discovered
superconductor Na_xCoO_2*yH_2O are studied based on a multi-orbital Hubbard
model. Tight-binding parameters are determined to reproduce the LDA band
dispersions with the Fermi surface, which consist of a large cylindrical one
around the Gamma-point and six hole pockets near the K-points. By applying the
fluctuation-exchange (FLEX) approximation, we show that the Hund's-rule
coupling between the Co t2g orbitals causes ferromagnetic (FM) spin
fluctuation. Triplet f_{y(y^2-3x^2)}-wave and p-wave pairings are favored by
this FM fluctuation on the hole-pocket band. We propose that, in
Na_xCoO_2*yH_2O, the Co t2g orbitals and inter-orbital Hund's-rule coupling
play important roles on the triplet pairing, and this compound can be a first
example of the triplet superconductor in which the orbital degrees of freedom
play substantial roles.
