On the Asymptotics of Takeuchi Numbers
| dc.creator | Prellberg, Thomas | |
| dc.date | 2000-05-01 | |
| dc.date.accessioned | 2026-07-07T04:34:56Z | |
| dc.date.available | 2026-07-07T04:34:56Z | |
| dc.description | I present an asymptotic formula for the Takeuchi numbers $T_n$. In particular, I give compelling numerical evidence and present a heuristic argument showing that $$T_n\sim C_T B_n\exp{1\over2}{W(n)}^2$$as $n$ tends to infinity, where $B_n$ are the Bell numbers, W(n) is Lambert's $W$ function, and $C_T=2.239...$ is a constant. Moreover, I show that the method presented here can be generalized to derive conjectures for related problems. | |
| dc.description | latex file with 13 pages, 2 postscript figures included | |
| dc.identifier | https://arxiv.org/abs/math/0005008 | |
| dc.identifier | http://arxiv.org/abs/math/0005008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59099 | |
| dc.subject | Combinatorics | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 05A16 | |
| dc.title | On the Asymptotics of Takeuchi Numbers | |
| dc.type | text |