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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

Table of n, a(n) for n=0..10.

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 November 12 17:06 EST 2019. Contains 329058 sequences. (Running on oeis4.)