As stated, the sequence is best described as that generated by
Un = (-8n5 + 135n4 - 812n3 + 2292n2 - 3047n + 1560)/6 for n = 1, 2, 3, ...
There would have been a much simpler solution IF the third number had been 30, but it is not so the above is your answer.
The number which best completes the sequence below is 20 5 30 6 42 7
56
The next number in the sequence will be 56.
1 2 2 6 3 12 4 20 5 30 6 42 7 56 8 72 9 90 10
56
56
54
56, 8, 72, 9
56
56
56, 8.
56 (just the next number, not the number that completes the sequence)