  064<p type="texpara" tag="Body Text" et="abstract" bin="clone" >In this
paper, we will consider an example of a (scalar-valued) moment series, under
the compatibility. Suppose that we have an amalgamated free product of free
group algebras, $L(F_{2})*_{L(F_{1})}L(F_{2})=L(<a,b>)*_{L(<h>)}L(<c,d>)$
  064<p type="texpara" tag="Body Text" et="abstract" bin="clone" >We will
provide the method how to find the moment series of
$a+b+a^{-1}+b^{-1}+c+d+c^{-1}+d^{-1}.$ Amalgamated freeness of
$a+b+a^{-1}+b^{-1}$ and $c+d+c^{-1}+d^{-1}$ over $L(F_{1})$ is used and some
combinatorial functions (to explain the recurrence relations) are used to
figure out the $n$-th moment of this element.
