  We consider the transform from sequences to triangular arrays defined in
terms of generating functions by f(x) -> (1-x)/(1-xy) f(x(1-x)/(1-xy)). We
establish a criterion for the transform of a nonnegative sequence to be
nonnegative, and we show that the transform counts certain classes of lattice
paths by number of "pyramid ascents", as well as certain classes of ordered
partitions by number of blocks that consist of increasing consecutive integers.
