  In a recent paper on a study of the Sylow 2-subgroups of the symmetric group
with 2^n elements it has been show that the growth of the first (n-2)
consecutive indices of a certain normalizer chain is linked to the sequence of
partitions of integers into distinct parts. Unrefinable partitions into
distinct parts are those in which no part x can be replaced with integers whose
sum is x obtaining a new partition into distinct parts. We prove here that the
(n-1)-th index of the previously mentioned chain is related to the number of
unrefinable partitions into distinct parts satisfying a condition on the
minimal excludant.
