The general rule behind the sequence is to write n! in base n.

For the first number, 2!=2, written in base 2 (binary) is 10.

For the second number, 3!=6, written in base 3 would be 20 (2*3^1 + 0*3^0).

For the third number, 4!=24, written in base 4 would be 120 (1*4^2 + 2*4^1 + 0*4^0).

For the last number (the ninth number), 10!=3628800, which written in base 10 is the same number.

Therefore, the answer is 3628800, or 10!.

If anyone wants to try with a computer, please post the solution you find. I think it would be interesting to see how a computer simulates human intuition.

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