Knights Tour - What is the relationship between board size and number of tours?

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I understand that the total number of Knights tours is known for boards up to 8 x 8.

These are: 1, 0, 0, 0, 1728, 6637920, 165575218320, 19591828170979904

As found here: "http://oeis.org/A165134"

Could some please explain the relationship between those numbers, or how they are increasing in relation to how board size increases.

Thanks.