Dominoes Covering

There are many ways to cover a chess board completely with \( 2 \times 1 \) dominos. In 1961, British physicist M.E.Fisher provedthat it can be done in 12988816 ways.

Now let us cut out two diagonally opposite corner squares. In how many ways can you cover the 62 squares of the mutilated chess board ?

Image credit: Wikipedia
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