A note on the reducibility of special infinite series

In this article we present how to reduce the evaluation of the special infinite series Sn=∑∞k=1kn(k+1)!, n=1,2,3,… which are very time consuming in Computer Algebra Systems (CAS). An algorithm is given for this purpose. Based on the new algorithm, a fast and reliable MAPLE procedure is designed and S1,S2,…,S50 are given as sample output of this procedure together with the cpu time.