On the Asymptotics of Takeuchi Numbers
نویسنده
چکیده
I present an asymptotic formula for the Takeuchi numbers Tn. In particular, I give compelling numerical evidence and present a heuristic argument showing that Tn ∼ CT Bn exp 1 2 W (n) as n tends to infinity, where Bn are the Bell numbers, W (n) is Lambert’s W function, and CT = 2.239 . . . is a constant. Moreover, I show that the method presented here can be generalized to derive conjectures for related problems. email: [email protected] Address after 1 June 2000: Institut für Theoretische Physik, Abteilung C, Technische Universität Clausthal, D-38678 Clausthal-Zellerfeld, Germany 1
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تاریخ انتشار 2008