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 A325850 Number of permutations of {1..n} whose differences of all degrees are nonzero. 5
 1, 1, 2, 4, 18, 72, 446, 2804, 21560, 184364, 1788514 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. LINKS EXAMPLE The a(1) = 1 through a(4) = 18 permutations:   (1)  (12)  (132)  (1243)        (21)  (213)  (1324)              (231)  (1342)              (312)  (1423)                     (2134)                     (2143)                     (2314)                     (2413)                     (2431)                     (3124)                     (3142)                     (3241)                     (3412)                     (3421)                     (4132)                     (4213)                     (4231)                     (4312) MATHEMATICA Table[Length[Select[Permutations[Range[n]], !MemberQ[Union@@Table[Differences[#, i], {i, Length[#]}], 0]&]], {n, 0, 5}] CROSSREFS Dominated by A295370, the case for only differences of degree 2. Cf. A049988, A175342, A238423, A279945, A325545, A325851, A325852, A325874, A325875. Sequence in context: A007727 A303352 A226011 * A052689 A139104 A014448 Adjacent sequences:  A325847 A325848 A325849 * A325851 A325852 A325853 KEYWORD nonn,more AUTHOR Gus Wiseman, May 31 2019 STATUS approved

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Last modified February 21 23:21 EST 2020. Contains 332113 sequences. (Running on oeis4.)