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It is possible to find infinitely many polynomials of order 5 such that the first five numbers are as listed in the question and any selected number is the next. There are also non-polynomial solutions.

The simplest polynomial of order 4 is

Un = (n^4 - 2n^3 + 11n^2 - 58n + 144)/24 for n = 1, 2, 3, ...

and accordingly, the next number in the sequence is 44.

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Q: The next number in the series 4 3 4 9 21?
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