Analysing problems of combinatorial nature arise naturally in the study of transformation semigroup. Combinatorial properties of many transformation semigroups and its subsemigroups have been studied with interesting and delightful results obtained. This paper investigated combinatorial properties on subsemigroup of order-decreasing alternating semigroups in which combinatorial functions and were used to derive some triangular arrays of numbers and some combinatorial results for each function were established. More so, the results on and were also obtained and generalized.