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Mar 9, 2013 at 2:06 comment added Brendan McKay And this leads to an explicit expression, see my answer (with nod to i707107).
Mar 8, 2013 at 21:20 comment added Sungjin Kim Yes. I checked it. Together with a property of this inverse matrix: Any column sum is 0 except for the last column, which is 1.
Mar 8, 2013 at 9:20 comment added Denis Serre Your guess is correct. It is not too difficult to check.
Mar 8, 2013 at 4:26 history edited Benjamin Young CC BY-SA 3.0
Added some sage code.
Mar 8, 2013 at 4:16 comment added Benjamin Young No problem - you're welcome.
Mar 8, 2013 at 2:02 comment added Yemon Choi My genuine thanks, by the way: I admit to being too technologically incompetent/lazy to stick the matrix into a CAS (more fool me), and as you observe the formula for the inverse is very suggestive. What it suggests to me is that this was indeed Mobius inversion ;-)
Mar 6, 2013 at 6:10 comment added Yemon Choi All informative answers are welcome. Note that I wasn't the person who used the word "enlightening" ;-)
Mar 6, 2013 at 5:21 history answered Benjamin Young CC BY-SA 3.0