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

1,2

Links

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

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

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 *)

Crossrefs

Cf. A028418, A046746, A006128.

Cf. A005225.

Column k=1 of A322383.

Sequence in context: A211193 A134018 A355719 * A060311 A184947 A330250

Adjacent sequences: A028414 A028415 A028416 * A028418 A028419 A028420

Keyword

nonn

Author

Joe Keane (jgk(AT)jgk.org)

Extensions

More terms from Vladeta Jovovic, Sep 19 2002

Status

approved