A346086 Number of permutations of [2n] such that the GCD of the cycle lengths equals 2.

0, 1, 3, 105, 4725, 530145, 45270225, 12034447425, 2116670180625, 737902583042625, 219604524727012425, 137952599116097390625, 49583382753435146240625, 46991310794950147391390625, 25508895927267586991297765625, 24661803286201363305440202410625

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..225

Wikipedia, Permutation

Formula

a(n) = A346085(2n,2).

Example

a(1) = 1: (12).
a(2) = 3: (12)(34), (13)(24), (14)(23).

Maple

b:= proc(n, g) option remember; `if`(n=0, `if`(g=2, 1, 0), `if`(g=1, 0,
       add(b(n-j, igcd(g, j))*binomial(n-1, j-1)*(j-1)!, j=2..n)))
    end:
a:= n-> b(2*n, 0):
seq(a(n), n=0..19);

Mathematica

b[n_, g_] := b[n, g] = If[n == 0, If[g == 2, 1, 0], If[g == 1, 0,
     Sum[b[n - j, GCD[g, j]]*Binomial[n - 1, j - 1]*(j - 1)!, {j, 2, n}]]];
a[n_] := b[2*n, 0];
Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Mar 06 2022, after Alois P. Heinz *)

Crossrefs

Bisection of column k=2 of A346085 (even part).

Sequence in context: A359988 A352408 A334776 * A271049 A101485 A226236

Adjacent sequences: A346083 A346084 A346085 * A346087 A346088 A346089

Keyword

nonn

Author

Alois P. Heinz, Jul 04 2021

Status

approved