  We solve the boson normal ordering problem for (q(a*)a + v(a*))^n with
arbitrary functions q and v and integer n, where a and a* are boson
annihilation and creation operators, satisfying [a,a*]=1. This leads to
exponential operators generalizing the shift operator and we show that their
action can be expressed in terms of substitutions. Our solution is naturally
related through the coherent state representation to the exponential generating
functions of Sheffer-type polynomials. This in turn opens a vast arena of
combinatorial methodology which is applied to boson normal ordering and
illustrated by a few examples.
