  Martin Klazar computed the total weight of ordered trees under 12 different
notions of weight. The last and perhaps most interesting of these weights,
w_{12}, led to a recurrence relation and an identity for which he requested
combinatorial explanations. Here we provide such explanations. To do so, we
introduce the notion of a "Klazar violator" vertex in an increasing ordered
tree and observe that w_{12} counts what we call Klazar trees--increasing
ordered trees with no Klazar violators. A highlight of the paper is a bijection
from n-edge increasing ordered trees to perfect matchings of [2n]={1,2,...,2n}
that sends Klazar violators to even numbers matched to a larger odd number. We
find the distribution of the latter matches and, in particular, establish the
one-summation explicit formula sum_{k=1}^{lfloor n/2 rfloor}(2k-1)!!^2
StirlingPartition{n+1}{2k+1} for the number of perfect matchings of [2n] with
no even-to-larger-odd matches. The proofs are mostly bijective.
