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

1,3

Links

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

Formula

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

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 *)

Crossrefs

Main diagonal of A222029.

Cf. A074351 (the same for permutations).

Sequence in context: A110729 A088258 A227886 * A089718 A123150 A086591

Adjacent sequences: A290958 A290959 A290960 * A290962 A290963 A290964

Keyword

nonn

Author

Alois P. Heinz, Aug 15 2017

Status

approved