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A028417 Sum over all n! permutations of n elements of minimum lengths of cycles. 10
1, 3, 10, 45, 236, 1505, 10914, 90601, 837304, 8610129, 96625970, 1184891081, 15665288484, 223149696601, 3394965018886, 55123430466945, 948479737691504, 17289345305870561, 332019600921360594, 6713316975465246889, 142321908843254560540, 3161718732648662557161 (list; graph; refs; listen; history; text; internal format)
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 *)

CROSSREFS

Cf. A028418, A046746, A006128.

Cf. A005225.

Column k=1 of A322383.

Sequence in context: A293554 A211193 A134018 * 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

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Last modified February 22 23:44 EST 2020. Contains 332157 sequences. (Running on oeis4.)