  From the unified statistical thermodynamics of quantum gases, the virial
coefficients of ideal Bose and Fermi gases which are trapped under generic
power law potential are derived systematically. From the general result of
virial coefficients, one can produce the known results in $d=3$ and $d=2$. But
more importantly we found that, the virial coefficients of bosons and fermions
become equal (except the the second virial coefficient, where the sign is
different) when we trap the gases under harmonic potential in $d=1$. This
result suggests the equivalence between Bose and Fermi gases which is already
established for $d=1$ by M M Faruk (J Stat Phys, DOI
10.1007/s10955-015-1344-4). Surprisingly our investigation also shows that the
virial coefficients of two dimensional free quantum gases are identical to the
virial coefficients of one dimensional harmonically trapped quantum gases.
