  We conjecture a simple set of "Feynman rules" for constructing $n$-point
global conformal blocks in any channel in $d$ spacetime dimensions, for
external and exchanged scalar operators for arbitrary $n$ and $d$. The vertex
factors are given in terms of Lauricella hypergeometric functions of one, two
or three variables, and the Feynman rules furnish an explicit power-series
expansion in powers of cross-ratios. These rules are conjectured based on
previously known results in the literature, which include four-, five- and
six-point examples as well as the $n$-point comb channel blocks. We prove these
rules for all previously known cases, as well as for a seven-point block in a
new topology and the even-point blocks in the "OPE channel." The proof relies
on holographic methods, notably the Feynman rules for Mellin amplitudes of
tree-level AdS diagrams in a scalar effective field theory, and is easily
applicable to any particular choice of a conformal block.
