Asymptotics for Morgan numbers of fractional orders

Morgan numbers of fractional orders are defined by the relation δkOn = ∑l=0k (−1)k−1klln, where k is an integer and n is a positive real number. Such numbers arose, quite unexpectedly, in our previous study of correlation properties of queueing lengths at arrival instants for multiphase queues with infinite number of channels in each phase. Here we consider asymptotics of these numbers and their relations to other combinatorial objects.