  For any function F(x) having a Taylor expansion we solve the boson normal
ordering problem for F[(a*)^r a^s], with r,s positive integers,[a,a*]=1, i.e.
we provide exact and explicit expressions for its normal form which has all a's
to the right. The solution involves integer sequences of numbers which, for r,s
>=1, are generalizations of the conventional Bell and Stirling numbers whose
values they assume for r=s=1. A complete theory of such generalized
combinatorial numbers is given including closed-form expressions (extended
Dobinski - type formulas), recursion relations and generating functions. These
last are special expectation values in boson coherent states.
