Logarithmic behavior of some combinatorial sequences |
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| Authors: | Tomislav Došli? Darko Veljan |
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| Institution: | a Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, Ka?i?eva 26, Zagreb, Croatia
b Department of Mathematics, University of Zagreb, Bijeni?ka 30, Zagreb, Croatia |
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| Abstract: | Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic behavior of some combinatorially relevant sequences, such as Motzkin and Schröder numbers, sequences of values of some classic orthogonal polynomials and many others. The calculus method extends also to numbers indexed by two or more parameters. |
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| Keywords: | 05A20 05A16 05E35 11B83 11B37 11B39 11B68 |
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