There are a lot of similar questions to this but none that is quite the same so I figured I would ask a new question. The problem is you have a group of people that came in pairs, in how many ways can the $N$ people be arranged in a circle such that no person in the circle is holding hands with the partner they came with.
I have worked out by hand that for two couples(four people) the answer is $2$ ways
For three couples ($6$ people) the answer is $32$ ways
Also it should be noted that a rotated circle is not counted as a different arrangement.
If the answer posted below is correct the OEIS sequence is http://oeis.org/A129348 Can any one else confirm that this is correct?