I see now how the answer is 1094. I made a mistake in my number computations. I had written:
original corrected correction made?
1) 8 0 0 1 1
2) 7 1 0 8 8
3) 6 2 0 28 28
4) 6 1 1 28 28
5) 5 3 0 56 56
6) 5 2 1 168 168
7) 4 4 0 70 35 Y
8) 4 3 1 280 280
9) 4 2 2 420 210 Y
10) 3 3 2 560 280 Y
So, I needed to correct #'s 7, 9, and 10. The original values I had were double what they should have been and I should have seen that right off because each of those has a repeated number (4, 2, and then 3 for case 7, 9, and then 10). So, if you add up my corrected column, you will get 1094, just like the Stirling numbers type 2 give you.
I never heard of the Stirling Numbers before and I'll have to read up on them. I did this the "long way", and you might want to go over my correction post here just to get an insight into how this has meaning. I could tell though, right off, that my method is definitely NOT the preferred method since it was so long and would be practical for only small numbers. This particular example is probably the largest anyone would ever want to do by hand or the "long way".
So, what I did was really the "guts" of the Stirling number type 2 and it gives the right answer IF you make no mistakes!