Is sequence A084894 plausible?

[Brendan McKay]

ID Number: A084894
Sequence:  0,0,2,20,112,696,5008,40280,362760,3628504,39916152,
           479000272,6227017600,8717828,1288,1307674342408,
           20922789832080,355687427952808,6402373705217304,
           1216451004073,80704,2432902008173142656
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!.

Brendan.