  We use strong coupling expansions to calculate the entropy function $S(T,h)$,
the magnetization $M(T,h)$, and the double occupancy factor $D(T,h)$ for the
half-filled triangular lattice Hubbard model as a function of temperature $T$
and Zeeman field $h$, for various values of the Hubbard parameter ratio $U/t$.
These calculations converge well for temperatures larger than the exchange
parameter $J=\frac{4t^2}{U}$ for moderate to large $U/t$ values. Setting
$\mu=U/2$ suffices to obtain the density of half filling within a fraction of
one percent at all temperatures studied for $U/t \geq 8$. We discuss the
systematic variation of properties with $U/t$. The temperature dependence of
entropy and the double occupancy parameter shows a mapping to an
antiferromagnetic Mott insulating behavior at temperatures well above $T=J$ for
$U/t\ge 10$. Convergence of the series is weaker at intermediate fields
implying non-monotonic variation of spin-correlations with the Zeeman field. We
discuss the relevance of the Hubbard model results to the triangular-lattice
antiferromagnetic materials Lu$_3$Cu$_2$Sb$_3$O$_{14} $ (LCSO) studied recently
by Yang et al [Yang et al arXiv:2102.09271 (2022)].
