On an open problem of Chen and Mortici concerning the Euler-Mascheroni constant

Chen and Mortici [Ch.-P. Chen, C. Mortici, New sequence converging towards the Euler-Mascheroni constant, Comput. Math. Appl. (2011); http://dx.doi.org/10.1016/j.camwa.2011.03.099] proposed an open problem: for a given positive integer s, find the constants ai(i=0,1,2,…,s) such that ∑k=1n1k−log(n+∑i=0sain−i) is the fastest sequence which would converge to the Euler-Mascheroni constant γ. Using logarithmic type Bell polynomials, we solve this problem. The main result shows that the ai's can be recursively determined.