  Ohno's relation states that a certain sum, which we call an Ohno type sum, of
multiple zeta values remains unchanged if we replace the base index by its dual
index. In view of Oyama's theorem concerning Ohno type sums of finite and
symmetric multiple zeta values, Kaneko looked at Ohno type sums of finite and
symmetric multiple zeta-star values and made a conjecture on the generating
function for a specific index of depth three. In this paper, we confirm this
conjecture and further give a formula for arbitrary indices of depth three.
