  We introduce a deformed version of Dyck paths (DDP), where additional to the
steps allowed for Dyck paths, 'jumps' orthogonal to the preferred direction of
the path are permitted. We consider the generating function of DDP, weighted
with respect to their half-length, area and number of jumps. This represents
the first example of an exactly solvable lattice path model showing a
higher-order multicritical point. Applying the generalized method of steepest
descents, we see that the associated two-variable scaling function is given by
the logarithmic derivative of a generalized (higher-order) Airy integral.
