  We conjecture a set of differential equations that characterizes the
Liouville irregular states of half-integer ranks, which extends the generalized
AGT correspondence to all the $(A_1,A_\text{even})$ and $(A_1,D_\text{odd})$
types Argyres-Douglas theories. For lower half-integer ranks, our conjecture is
verified by deriving it as a suitable limit of a similar set of differential
equations for integer ranks. This limit is interpreted as the 2D counterpart of
a 4D RG-flow from $(A_1,D_{2n})$ to $(A_1,D_{2n-1})$. For rank $3/2$, we solve
the conjectured differential equations and find a power series expression for
the irregular state $|I^{(3/2)}\rangle$. For rank $5/2$, our conjecture is
consistent with the differential equations recently discovered by H. Poghosyan
and R. Poghossian.
