  We compute topological one-point functions of the chiral operator Tr \phi^k
in the maximally confining phase of U(N) supersymmetric gauge theory. These
one-point functions are polynomials in the equivariant parameter \hbar and the
parameter of instanton expansion q=\Lambda^{2N} and are of particular interest
from gauge/string theory correspondence, since they are related to the
Gromov-Witten theory of P^1. Based on a combinatorial identity that gives
summation formula over Young diagrams of relevant functions, we find a relation
among chiral one-point functions, which recursively determines the \hbar
expansion of the generating function of one-point functions. Using a result
from the operator formalism of the Gromov-Witten theory, we also present a
vacuum expectation value of the loop operator Tr e^{it\phi}.
