  Large $N$ melonic theories are characterized by two-point function Feynman
diagrams built exclusively out of melons. This leads to conformal invariance at
strong coupling, four-point function diagrams that are exclusively ladders, and
higher-point functions that are built out of four-point functions joined
together. We uncover an incredibly useful property of these theories: the
six-point function, or equivalently, the three-point function of the primary
$O(N)$ invariant bilinears, regarded as an analytic function of the operator
dimensions, fully determines all correlation functions, to leading nontrivial
order in $1/N$, through simple Feynman-like rules. The result is applicable to
any theory, not necessarily melonic, in which higher-point correlators are
built out of four-point functions. We explicitly calculate the bilinear
three-point function for $q$-body SYK, at any $q$. This leads to the bilinear
four-point function, as well as all higher-point functions, expressed in terms
of higher-point conformal blocks, which we discuss. We find universality of
correlators of operators of large dimension, which we simplify through a saddle
point analysis. We comment on the implications for the AdS dual of SYK.
