Search: id:A038205
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%I A038205
%S A038205 1,0,0,2,6,24,160,1140,8988,80864,809856,8907480,106877320,1389428832,
%T A038205 19452141696,291781655984,4668504894480,79364592318720,1428562679845888,
%U A038205 27142690734936864,542853814536802656,11399930109077490560
%N A038205 Number of derangements of n where minimal cycle size is at least 3.
%C A038205 Permutations with no cycles of length 1 or 2.
%C A038205 Related to (and bounded by) "derangements" (A000166). Minimal cycle size 
               3 is interesting because of its physical analog. Consider a fully-connected 
               network of n nodes where the objects stored at the nodes must derange 
               but can't do so in such a way that any two objects would collide 
               along the connecting "pipe" between their nodes.
%D A038205 H. S. Wilf, Generatingfunctionology, Academic Press, NY, 1990, p. 147, 
               Eq. 5.2.9 (q=2).
%D A038205 G. Paquin, D\'enombrement de multigraphes enrichis, M\'emoire, Math. 
               Dept., Univ. Qu\'ebec \`a Montr\'eal, 2004.
%H A038205 H. S. Wilf, <a href="http://www.math.upenn.edu/~wilf/DownldGF.html">Generatingfunctionology</
               a>, 2nd edn., Academic Press, NY, 1994, p. 176, Eq. 5.2.9 (q=2).
%F A038205 a(n) = Sum C(n-1, i-1)(i-1)!a(n-i), i = 3 ... n. E.g.f.: exp(-x-x^2/2)/
               (1-x).
%e A038205 a(5) = 24 because, with a minimum cycle size of 3, the only way to derange 
               all 5 elements is to have them move around in one large 5-cycle. 
               The number of possible moves is (5-1)! = 4! = 24.
%p A038205 ZL2:=[S,{S=Set(Cycle(Z,card>2))},labeled] :seq(count(ZL2,size=n),n=0..21); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 26 2007
%p A038205 with (combstruct):a:=proc(m) [ZZ,{ZZ=Set(Cycle(Z,card>m))},labeled]; 
               end: A038205:=a(2):seq(count(A038205,size=n),n=0..21); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Oct 02 2007
%Y A038205 Cf. A047865, A000166.
%Y A038205 Sequence in context: A013010 A009608 A012715 this_sequence A012361 A121773 
               A012711
%Y A038205 Adjacent sequences: A038202 A038203 A038204 this_sequence A038206 A038207 
               A038208
%K A038205 nonn,easy,nice
%O A038205 0,4
%A A038205 Charles G. Moore (cmoore(AT)microsoft.com), N. J. A. Sloane (njas(AT)research.att.com).
%E A038205 Definition corrected by Brendan McKay, Jun 02 2007

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