Write an explicit formula for the sequence:
{18,19,110,111,112,113,}\displaystyle {\left\lbrace\frac{{1}}{{8}},-\frac{{1}}{{{9}}},\frac{{1}}{{{10}}},-\frac{{1}}{{{11}}},\frac{{1}}{{{12}}},-\frac{{1}}{{{13}}},\ldots\right\rbrace}
an=\displaystyle {a}_{{n}}=