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Given any number it is easy to find a rule based on a polynomial of order 7 such that the first seven numbers are as listed in the question and the next is the given number.
The simplest polynomial of order 6 is
Un = (-14n6 + 336n5 - 3185n4 + 15120n3 - 37436n2 + 45069n - 19170)/90 for n = 1, 2, 3, ...
Accordingly, the next term is -209.
You may, of course, be looking for a non-polynomial solution, and there are infinitely many of those.
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