  We derive a recursion relation for the analytic leading logarithmic
coefficients of a final state gluon cascade. We demonstrate the potential of
our method by analytically computing the rate coefficients for the emission of
up to 80 gluons in both the exclusive-kT (Durham) and generalized inclusive-kT
class of jet algorithms. There is a particularly simple form for the ratios of
resolved coefficients. We suggest potential applications including the
efficient generation of shower histories.
