Some Baer invariants of free nilpotent groups

We present an explicit structure for the Baer invariant of a free nth nilpotent group (the nth nilpotent product of infinite cyclic groups, ) with respect to the variety V with the set of words V={[γc1+1,γc2+1]}, for all c1⩾c2 and 2c2−c1>2n−2. Also, an explicit formula for the polynilpotent multiplier of a free nth nilpotent group is given for any class row (c1,c2,…,ct), where c1⩾n.