  A numerical semigroup is a sub-semigroup of the natural numbers that has a
finite complement. Some of the key properties of a numerical semigroup are its
Frobenius number F, genus g and type t. It is known that for any numerical
semigroup $\frac{g}{F+1-g}\leq t\leq 2g-F$. Numerical semigroups with $t=2g-F$
are called almost symmetric, we introduce a new property that characterises
them. We give an explicit characterisation of numerical semigroups with
$t=\frac{g}{F+1-g}$. We show that for a fixed $\alpha$ the number of numerical
semigroups with Frobenius number $F$ and type $F-\alpha$ is eventually constant
for large $F$. Also the number of numerical semigroups with genus $g$ and type
$g-\alpha$ is also eventually constant for large $g$.
