2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59099I 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.latex file with 13 pages, 2 postscript figures includedCombinatoricsClassical Analysis and ODEs05A16text