In this paper, we introduce
k
k
-Young tableaux and their
g
g
-indices. We first present certain expansions of
(
c
(
x
)
D
)
n
(c(x)D)^n
in terms of inversion sequences as well as
k
k
-Young tableaux, where
c
(
x
)
c(x)
is a smooth function in the indeterminate
x
x
and
D
D
is the derivative with respect to
x
x
. By studying the connections between
k
k
-Young tableaux and standard Young tableaux, we then present combinatorial interpretations of Eulerian polynomials, second-order Eulerian polynomials, and André polynomials in terms of standard Young tableaux.