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A208231 Sum of the minimum cycle length over all functions f:{1,2,...,n}->{1,2,...,n} (endofunctions).

%I A208231 #25 Aug 16 2017 15:31:33
%S A208231 0,1,5,37,373,4761,73601,1336609,27888281,657386305,17276807089,
%T A208231 500876786301,15879053677697,546470462226313,20288935994319929,
%U A208231 808320431258439121,34397370632215764001,1557106493482564625793,74713970491718324746529,3787792171563440619543133,202314171910557294992453009
%N A208231 Sum of the minimum cycle length over all functions f:{1,2,...,n}->{1,2,...,n} (endofunctions).
%C A208231 Sum of the number of endofunctions whose cycle lengths are >=i for all i >=1.  A000312 + A065440 + A134362 + A208230 + ...
%H A208231 Alois P. Heinz, <a href="/A208231/b208231.txt">Table of n, a(n) for n = 0..386</a>
%F A208231 E.g.f.: A(T(x)) = Sum_{k>=1} exp( Sum_{i>=k} T(x)^i/i) - 1  where A(x) is the e.g.f. for A028417 and T(x) is the e.g.f. for A000169.
%p A208231 b:= proc(n, m) option remember; `if`(n=0, m, add((j-1)!*
%p A208231       b(n-j, min(m, j))*binomial(n-1, j-1), j=1..n))
%p A208231     end:
%p A208231 a:= n-> add(b(j$2)*n^(n-j)*binomial(n-1, j-1), j=0..n):
%p A208231 seq(a(n), n=0..25);  # _Alois P. Heinz_, May 20 2016
%t A208231 nn=20;t=Sum[n^(n-1)x^n/n!,{n,1,nn}];Apply[Plus,Table[Range[0,nn]!CoefficientList[Series[Exp[Sum[t^i/i,{i,n,nn}]]-1,{x,0,nn}],x],{n,1,nn}]]
%Y A208231 Cf. A000169, A028417, A000312, A065440, A134362, A208230, A208248, A290932.
%K A208231 nonn
%O A208231 0,3
%A A208231 _Geoffrey Critzer_, Jan 10 2013