ClearAll[DominoTilingCount]
DominoTilingCount[m_, n_] := Module[{},
  Round[Product[
    4 Cos[(Pi j)/(m + 1)]^2 + 4 Cos[(Pi k)/(n + 1)]^2,
     {j, Ceiling[m/2]},
     {k, Ceiling[n/2]}
   ]]
]
arrangements = DominoTilingCount[7, 8] // Round;
permutations = 28!;
flips = 2^28;
Print["Arrangements ignoring values: ", arrangements]
Print["Permutations of 28 dominos: ", permutations]
Print["Permuted arrangements ignoring flipping dominos: ", arrangements*permutations]
Print["Possible flip configurations: ", flips]
Print["Possible permuted arrangements with flips: ", flips*arrangements*permutations]