  Polynomial sequences $p_n(x)$ of binomial type are a principal tool in the
umbral calculus of enumerative combinatorics. We express $p_n(x)$ as a
\emph{path integral} in the ``phase space'' $\Space{N}{} \times {[-\pi,\pi]}$.
The Hamiltonian is $h(\phi)=\sum_{n=0}^\infty p_n'(0)/n! e^{in\phi}$ and it
produces a Schr\"odinger type equation for $p_n(x)$. This establishes a bridge
between enumerative combinatorics and quantum field theory. It also provides an
algorithm for parallel quantum computations.
  Keywords: Feynman path integral, umbral calculus, polynomial sequence of
binomial type, token, Schr\"odinger equation, propagator, wave function,
cumulants, quantum computation.
