Is sequence A084894 plausible?

Brendan McKay bdm at
Mon Sep 6 09:39:22 CEST 2004

ID Number: A084894
Sequence:  0,0,2,20,112,696,5008,40280,362760,3628504,39916152,
Name:      Number of permutations of length n such that at least one absolute
              difference between consecutive elements has a distinct partner.
Comments:  a(n)=n!-A006967(n)

I suggest that this sequence is broken as the small values interspersed
with the large values are impossible.  Sequence A006967 (graceful
permutations) is ok.  Graceful permutations are a vanishing fraction
of all permutations so A084894(n) should be close to n!.


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