  A stabilized-interval-free (SIF) permutation on [n]={1,2,...,n} is one that
does not stabilize any proper subinterval of [n]. By presenting a decomposition
of an arbitrary permutation into a list of SIF permutations, we show that the
generating function A(x) for SIF permutations satisfies the defining property:
[x^(n-1)] A(x)^n = n! . We also give an efficient recurrence for counting SIF
permutations.
