A324376 Number of permutations p of [n] whose absolute displacements |p(i)-i| are factorial numbers.

1, 0, 1, 2, 4, 6, 13, 48, 149, 286, 832, 2304, 6560, 13630, 35937, 95816, 242496, 586480, 1492057, 3928292, 10019073, 24819960, 63656169, 163618614, 416809221, 1731461192, 6214212533

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Wikipedia, Permutation

Example

a(2) = 1: 21.
a(3) = 2: 231, 312.
a(4) = 4: 2143, 2413, 3142, 3412.
a(5) = 6: 21453, 21534, 23154, 24153, 31254, 31524.
a(6) = 13: 214365, 214635, 215364, 215634, 231564, 231645, 241365, 241635, 312564, 312645, 314265, 315264, 341265.

Maple

g:= proc(n) local i; 1; for i from 2 do
      if n=% then true; break elif n<% then false; break fi;
      %*i od; g(n):=%
    end:
b:= proc(s) option remember; (n-> `if`(n=0, 1, add(`if`(
      g(abs(n-j)), b(s minus {j}), 0), j=s)))(nops(s))
    end:
a:= n-> b({$1..n}):
seq(a(n), n=0..20);

Mathematica

factorialQ[n_] := factorialQ[n] = Module[{i, k = 1}, For[i = 2, True, i++, If[n == k, Return[True]]; If[n < k, Return[False]]; k = k*i]];
b[s_] := b[s] = With[{n = Length[s]}, If[n == 0, 1, Sum[If[factorialQ[Abs[n - j]], b[s ~Complement~ {j}], 0], {j, s}]]];
a[n_] := b[Range[n]];
a /@ Range[0, 20] (* Jean-François Alcover, Mar 25 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000142, A324372, A324373, A324374, A324375.

Sequence in context: A295618 A346407 A369390 * A027712 A282139 A138307

Adjacent sequences: A324373 A324374 A324375 * A324377 A324378 A324379

Keyword

nonn

Author

Alois P. Heinz, Feb 25 2019

Status

approved