  The number of conjugate classes of derangements of order $n$ is the same as
the number $h(n)$ of the restricted partitions with every portion greater than
$1$. It is also equal to the number of isotopy classes of $2\times n$ Latin
rectangles. Sometimes the exact value is necessary, while sometimes we need the
approximation value. In this paper, a recursion formula of $h(n)$ will be
obtained, also will some elementary approximation formulae with high accuracy
for $h(n)$ be presented. Although we may obtain the value of $h(n)$ in some
computer algebra system, it is still meaningful to find an efficient way to
calculate the approximate value, especially in engineering, since most people
are familiar with neither programming nor CAS software. This paper is mainly
for the readers who need a simple and practical formula to obtain the
approximate value (without writing a program) with more accuracy, such as to
compute the value in an pocket science calculator without programming function.
Some methods used here can also be applied to find the fitting functions for
some types of data obtained in experiments.
