Question: Can you work out how this number sequence is built up? Can you work out how it continues? 

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> 1, 1, 2, 4, 8, 20, 60, 240, 1500, .......
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*Hint 1*

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>  this is a mathematical puzzle
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*Hint 2*

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>  It does not involve complicated mathematics
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*From time to time hints will be updated.*

*Note: this sequence cannot be found in [The On-Line Encyclopedia of Integer Sequences](https://oeis.org/)*

Answer: 
The next number is

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>  16140
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Following this pattern, given the sequence is $a\_n$

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>  $a\_n = a\_{n-1} + a\_{n-2} \cdot (a\_{n-3} + 1)$  
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>  Example: 60 = 20 + 8 \* (4 + 1)
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Obligatory nth order polynomial:

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> $$f(x) = \frac{5}{384}x^8-\frac{4597}{10080}x^7+\frac{19471}{2880}x^6 - \frac{19831}{360}x^5+\frac{308935}{1152}x^4-\frac{1141669}{1440}x^3+\frac{1982957}{1440}x^2-\frac{354937}{280}+465$$
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Predicted next five values:

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> 8116, 33619, 112289, 318913, 800021
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