0,1,3,9,33,( )

The given sequence is 0, 1, 3, 9, 33, ( ). To find the next term, we examine the differences between consecutive terms:

[

begin{align}

33

end{align}

]

These differences (1, 2, 6, 24) correspond to the factorials of 1, 2, 3, and 4 respectively. The next difference should be the factorial of 5, which is (5! = 120).

Adding this to the last term in the sequence:

[

33 + 120 = 153.

]

To verify, each term in the sequence is the sum of all factorials up to ( (n-1)! ) where ( n ) is the term's position. For example, the fifth term is the sum of factorials from 1! to 4!:

[

1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33.

]

Following this pattern, the sixth term is the sum of factorials from 1! to 5!:

[

1! + 2! + 3! + 4! + 5! = 1 + 2 + 6 + 24 + 120 = 153.

]

Thus, the next number in the sequence is (boxed{153}).