Is sequence A084894 plausible?

Pfoertner, Hugo Hugo.Pfoertner at
Mon Sep 6 10:49:35 CEST 2004

>-----Original Message-----
>From: Brendan McKay [mailto:bdm at] 
>Sent: Monday, September 06, 2004 09:39
>To: seqfan at
>Subject: Is sequence A084894 plausible?
>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!.

Seems to be the usual line-wrap mess when using the submission form

See the FAQ's: "Q: A comma appeared in the middle of a number in my sequence
- why?"

The correct sequence should be:

The interspersed small values "1288" and "80704" just have to be
concatenated with
the preceding entries to get what the comment says.


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