A290961 Number of endofunctions on [n] such that the LCM of their cycle lengths equals n.

1, 1, 2, 6, 24, 840, 720, 5040, 40320, 59814720, 3628800, 83701537920, 479001600, 26980643289600, 2642646473026560, 1307674368000, 20922789888000, 41837259585747225600, 6402373705728000, 598354114828973074790400, 18160977780223038067507200

Offset: 1

Author

Alois P. Heinz, Aug 15 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..389

Crossrefs

Main diagonal of A222029.

Cf. A074351 (the same for permutations).

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, x^m, add((j-1)!*
      b(n-j, ilcm(m, j))*binomial(n-1, j-1), j=1..n))
    end:
a:= n-> add(coeff(b(j, 1), x, n)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=1..25);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, x^m, Sum[(j - 1)!*
     b[n - j, LCM[m, j]]*Binomial[n - 1, j - 1], {j, 1, n}]];
a[n_] := Sum[Coefficient[b[j, 1], x, n]*n^(n-j)*Binomial[n-1, j-1], {j, 0, n}];
Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Mar 07 2022, after Alois P. Heinz *)

Formula

a(n) = A222029(n,n).