A333892 Number of permutations sigma of [n] such that i divides Product_{k=1..i} sigma(k) for 1 <= i <= n.

1, 1, 2, 4, 14, 36, 320, 1328, 7872, 51552, 756480, 5440752, 68999136, 584117952, 9632932800, 152699071104, 1881048314880, 21977611223040, 343998708042240, 4374197540536320, 77078374650869760, 1646804888482037760, 45052372505959096320, 727420047420178022400

Offset: 0

Author

Seiichi Manyama, Apr 09 2020

Keywords

• nonn

Examples

			a(5) = 36: 12345, 14325, 14352, 21345, 23145, 23415, 23451, 23541, 24315, 24351, 25341, 32145, 32415, 32451, 32541, 34125, 34152, 34215, 34251, 34512, 34521, 41325, 41352, 42315, 42351, 43125, 43152, 43215, 43251, 43512, 43521, 45312, 45321, 52341, 54312, 54321.
		

Crossrefs

Cf. A320843, A333710.

Programs

Maple

b:= proc(s) option remember; (n-> `if`(n=0, 1, `if`(irem(
      mul(i, i=s), n)=0, add(b(s minus {j}), j=s), 0)))(nops(s))
    end:
a:= n-> b({$1..n}):
seq(a(n), n=0..17);  # Alois P. Heinz, Apr 09 2020

Mathematica

b[s_] := b[s] = With[{n = Length[s]}, If[n==0, 1, If[Mod[Times@@s, n]==0, Sum[b[s ~Complement~ {j}], {j, s}], 0]]];
a[n_] := b[Range[n]];
a /@ Range[0, 20] (* Jean-François Alcover, Nov 16 2020, after Alois P. Heinz *)

PARI

{a(n) = if(n==0, 1, my(k=0); forperm([1..n], p, if(#Set(vector(n, i, prod(j=1, i, p[j])%i))==1, k++)); k)}

Extensions

a(0), a(13)-a(23) from Alois P. Heinz, Apr 09 2020