Permutations, Adjacents Have Near-by Binary 1's

[Max]

Leroy Quet wrote:
> 
> Take the integers 1 through n written in binary.
> The nth term of the sequence is the number of permutations of these 
> binary numbers such that every 1-digit in the kth element (2<=k<=n) of 
> the permutation is either in the same position as, is one position to the 
> left of, or is one position to the right of a 1-digit in the (k-1)th 
> element written in binary.

[...]

> I get that the sequence of number of such permutations for 1 through n
> begins 1, 2, 6, 8,...

I've got
1 2 6 8 24 168 840 1008 4032 32160 192960 1297440 9082080 126846720 1141620480 1243468800 4490307360 53812332000 526257365760 3736568586240

and respectively the number of circular permutations of this kind (up to rotations):
1 1 2 1 2 18 72 42 126 1080 5400 42240 253440 3578400 28627200 16914240 54396720 620978400 5417102880 40328285760

Max