Is there an explicit formula for the index of regularity of a generic Hilbert function in two variables? (i.e., the Hilbert function of an ideal of $k[X,Y]$ generated by $r$ generic forms $f_{i}$ of degrees $d_{i}\geq 1$).
A result of R. Froberg (Math. Scand. 56 (1985) 117-144) characterizes the generic index of regularity as the first value when some known function of $d\in\mathbf{N}$ turns nonpositive, but that's not an explicit formula (an explicit formula should give the answer in terms of $r$ and $d_{1},...,d_{r}$ and nothing else).
