A028417 Sum over all n! permutations of n elements of minimum lengths of cycles.

1, 3, 10, 45, 236, 1505, 10914, 90601, 837304, 8610129, 96625970, 1184891081, 15665288484, 223149696601, 3394965018886, 55123430466945, 948479737691504, 17289345305870561, 332019600921360594, 6713316975465246889, 142321908843254560540, 3161718732648662557161

Offset: 1

Author

Joe Keane (jgk(AT)jgk.org)

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..450

Crossrefs

Cf. A028418, A046746, A006128.

Cf. A005225.

Column k=1 of A322383.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, m, add((j-1)!*
      b(n-j, min(m,j))*binomial(n-1, j-1), j=1..n))
    end:
a:= n-> b(n, infinity):
seq(a(n), n=1..25);  # Alois P. Heinz, May 14 2016

Mathematica

Drop[Apply[Plus,Table[nn=25;Range[0,nn]!CoefficientList[Series[Exp[Sum[ x^i/i,{i,n,nn}]]-1,{x,0,nn}],x],{n,1,nn}]],1] (* Geoffrey Critzer, Jan 10 2013 *)
b[n_, m_] := b[n, m] = If[n == 0, m, Sum[(j-1)! b[n-j, Min[m, j]]* Binomial[n-1, j-1], {j, n}]];
a[n_] := b[n, Infinity];
Array[a, 25] (* Jean-François Alcover, Apr 21 2020, after Alois P. Heinz *)

Formula

E.g.f.: Sum[k>0, -1+ exp(Sum(j>=k, x^j/j))]. - Vladeta Jovovic, Jul 26 2004

a(n) = Sum_{k=1..n} k * A145877(n,k). - Alois P. Heinz, Jul 28 2014

Extensions

More terms from Vladeta Jovovic, Sep 19 2002