Wang, Weiping; Wang, Tianming An automatic approach to the generating functions of some special sequences. (English) Zbl 1340.05004 Ars Comb. 116, 263-278 (2014). Summary: In this paper, we give explicit algorithms to compute generating functions of some special sequences, based on the operations of differential operators and shift operators in the non-commutative context and Zeilberger’s holonomic algorithm. It can be found that not only ordinary generating functions and exponential generating functions but also generating functions of the general form \(\sum_n a_n(x)\omega (y,n)\) can now be computed automatically. Moreover, we generalize this approach and present explicit algorithms to compute 2-variable ordinary power series generating functions and mixed-type generating functions. As applications, various examples are given in the paper. MSC: 05A15 Exact enumeration problems, generating functions Keywords:computer proof; generating function; holonomic function; Zeilberger’s holonomic algorithm PDFBibTeX XMLCite \textit{W. Wang} and \textit{T. Wang}, Ars Comb. 116, 263--278 (2014; Zbl 1340.05004)