A370514 Number of permutations p of [n] such that for each distance d in [n-1] there is at least one index i in [n-d] with p(i)>p(i+d).

1, 1, 1, 3, 11, 55, 319, 2233, 17641, 158769, 1578667, 17365337, 207865289, 2702248757, 37786779669, 566801695035, 9063808803203, 154084749654451

Offset

0,4

Links

Table of n, a(n) for n=0..17.

Wikipedia, K-sorted sequence

Wikipedia, Permutation

Formula

a(n) = A370507(n,n).

a(n) = A370506(n,1) for n>=1.

Example

a(0) = 1: the empty permutation.
a(1) = 1: 1.
a(2) = 1: 21.
a(3) = 3: 231, 312, 321.
a(4) = 11: 2341, 2431, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, 4321.
a(5) = 55: 23451, 23541, 24351, 24531, ..., 54213, 54231, 54312, 54321.
a(6) = 319: 234561, 234651, 235461, 235641, ..., 654213, 654231, 654312, 654321.

Crossrefs

Main diagonal of A370507.

Column k=1 of A370506 (for n>=1).

Cf. A008302.

Sequence in context: A094259 A091845 A020061 * A330041 A125696 A001776

Adjacent sequences: A370511 A370512 A370513 * A370516 A370517 A370518

Keyword

nonn,more

Author

Alois P. Heinz, Feb 20 2024

Extensions

a(14)-a(16) from Martin Ehrenstein, Feb 22 2024

a(17) from Alois P. Heinz, Feb 22 2024

Status

approved