Deranged numbers

The pattern starts with 0, then the next number is (0×2)+1 = 1. The next number is (1×3)-1 = 2. The next number is (2×4)+1 = 9. The next number is (9×5)-1 = 44. The next number is (44 × 6)+1 = 265. So, the next number should be (265×7)-1 = $\boxed{1854}$ . In the pattern, the previous number is multiplied by a number which is one more than what was multiplied to the previous number, then from the product one is alternatively subtracted and added.

The series represents $!n$ , where $!n$ is the "derangement number" or the number of ways you can rearrange $n$ distinct objects such that no object winds up in the same position. $!7 = \boxed{1854}$