  We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$
at stage $n$ with dimension $d$ equal to two, three, four or five, where one of
the outmost vertices is not covered when the number of vertices $v(n)$ is an
odd number. The entropy of absorption of diatomic molecules per site, defined
as $S_{SG_d}=\lim_{n \to \infty} \ln N_d(n)/v(n)$, is calculated to be
$\ln(2)/3$ exactly for $SG_2(n)$. The numbers of dimers on the generalized
Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4,5$ are also obtained
exactly. Their entropies are equal to $\ln(6)/7$, $\ln(28)/12$, $\ln(200)/18$,
respectively. The upper and lower bounds for the entropy are derived in terms
of the results at a certain stage for $SG_d(n)$ with $d=3,4,5$. As the
difference between these bounds converges quickly to zero as the calculated
stage increases, the numerical value of $S_{SG_d}$ with $d=3,4,5$ can be
evaluated with more than a hundred significant figures accurate.
