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It is easy to find a rule based on a polynomial of order 5 such that these numbers are the first five generated by the rule. There are also non-polynomial solutions.

A solution based on a polynomial of order 4 is

Un = (103n4 - 1242n3 + 5201n2 - 8670n + 4680)/24 for n = 1, 2, ..., 5.

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