Each number in this table has a significance, and it is not just the property of the individual number.

What statement might define the right for each to appear?

1 1 1 2 4 4 3 9 9 13 169 16 67 4489 25 264 69696 36 1667 2778889 49 .. ... 64

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That said, is it possible (and how) to analytically define the precise numerical values of successive rows?