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A325850 Number of permutations of {1..n} whose differences of all degrees are nonzero. 7

%I

%S 1,1,2,4,18,72,446,2804,21560,184364,1788514

%N Number of permutations of {1..n} whose differences of all degrees are nonzero.

%C The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) are (-3,-2). The zeroth differences are the sequence itself, while k-th differences for k > 0 are the differences of the (k-1)-th differences. The differences of all degrees of a sequence are the union of its zeroth through m-th differences, where m is the length of the sequence.

%e The a(1) = 1 through a(4) = 18 permutations:

%e (1) (12) (132) (1243)

%e (21) (213) (1324)

%e (231) (1342)

%e (312) (1423)

%e (2134)

%e (2143)

%e (2314)

%e (2413)

%e (2431)

%e (3124)

%e (3142)

%e (3241)

%e (3412)

%e (3421)

%e (4132)

%e (4213)

%e (4231)

%e (4312)

%t Table[Length[Select[Permutations[Range[n]],!MemberQ[Union@@Table[Differences[#,i],{i,Length[#]}],0]&]],{n,0,5}]

%Y Dominated by A295370, the case for only differences of degree 2.

%Y Cf. A049988, A175342, A238423, A279945, A325545, A325851, A325852, A325874, A325875.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, May 31 2019

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Last modified April 5 16:04 EDT 2020. Contains 333245 sequences. (Running on oeis4.)