A290932 Sum of the LCM of cycle lengths over all endofunctions on [n].

1, 1, 5, 40, 431, 5886, 96817, 1862890, 41043375, 1018584610, 28108489541, 853617865134, 28287119604955, 1015630741097350, 39273014068691145, 1627118268024495586, 71904849762914854703, 3375959341815207350850, 167810405947367539063885, 8803814897608815310714270

Offset: 0

Author

Alois P. Heinz, Aug 13 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Crossrefs

Cf. A000793, A060014, A208231, A208248, A222029.

Programs

Maple

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

Mathematica

T[n_, k_] := T[n, k] = If[n == 0, k, Sum[(j - 1)! * T[n - j, LCM[k, j]]*Binomial[n - 1, j - 1], {j, n}]]; {1}~Join~Table[Sum[T[j, 1]*n^(n - j)*Binomial[n - 1, j - 1], {j, 0, n}], {n, 19}] (* Michael De Vlieger, Aug 17 2017 *)

Formula

a(n) = Sum_{k=1..A000793(n)} k * A222029(n,k).