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A028417 Sum over all n! permutations of n elements of minimum lengths of cycles. 10


%S 1,3,10,45,236,1505,10914,90601,837304,8610129,96625970,1184891081,

%T 15665288484,223149696601,3394965018886,55123430466945,

%U 948479737691504,17289345305870561,332019600921360594,6713316975465246889,142321908843254560540,3161718732648662557161

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

%H Alois P. Heinz, <a href="/A028417/b028417.txt">Table of n, a(n) for n = 1..450</a>

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

%F a(n) = Sum_{k=1..n} k * A145877(n,k). - _Alois P. Heinz_, Jul 28 2014

%p b:= proc(n, m) option remember; `if`(n=0, m, add((j-1)!*

%p b(n-j, min(m,j))*binomial(n-1, j-1), j=1..n))

%p end:

%p a:= n-> b(n, infinity):

%p seq(a(n), n=1..25); # _Alois P. Heinz_, May 14 2016

%t 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 *)

%t 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}]];

%t a[n_] := b[n, Infinity];

%t Array[a, 25] (* _Jean-Fran├žois Alcover_, Apr 21 2020, after _Alois P. Heinz_ *)

%Y Cf. A028418, A046746, A006128.

%Y Cf. A005225.

%Y Column k=1 of A322383.

%K nonn

%O 1,2

%A Joe Keane (jgk(AT)jgk.org)

%E More terms from _Vladeta Jovovic_, Sep 19 2002

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Last modified June 23 12:00 EDT 2021. Contains 345400 sequences. (Running on oeis4.)