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URL: https://oeis.org/A028417

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A028417
Sum over all n! permutations of n elements of minimum lengths of cycles.
11
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
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. A005225.
Column k=1 of A322383.
Sequence in context: A211193 A134018 A355719 * A060311 A184947 A330250
KEYWORD
nonn
AUTHOR
Joe Keane (jgk(AT)jgk.org)
EXTENSIONS
More terms from Vladeta Jovovic, Sep 19 2002
STATUS
approved