%I A000387 M4138 N1716
%S A000387 1,0,6,20,135,924,7420,66744,667485,7342280,88107426,1145396460,
%T A000387 16035550531,240533257860,3848532125880,65425046139824,1177650830516985,
%U A000387 22375365779822544,447507315596451070,9397653627525472260,206748379805560389951
%N A000387 Rencontres numbers: permutations with exactly two fixed points.
%C A000387 Also: odd permutations of length n with no fixed points. - Martin Wohlgemuth 
               (mail(AT)matroid.com), May 31 2003
%C A000387 Also number of cycles of length 2 in all derangements of [n]. Example: 
               a(4)=6 because in the derangements of [4], namely (1432), (1342), 
               (13)(24), (1423), (12)(34), (1243), (1234), (1324), and (14)(23), 
               we have altogether 6 cycles of length 2. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Mar 31 2009]
%D A000387 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000387 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000387 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               65.
%H A000387 M. Wohlgemuth <a href="http://matheplanet.com/matheplanet/nuke/html/print.php?sid=444">
               Derangements revisited</a>
%F A000387 a(n) = sum((-1)^j*n!/(2!*j!), j=2..n-2)
%F A000387 a(n) = A000166(n-2)*binomial(n, 2). - David Wasserman (wasserma(AT)spawar.navy.mil), 
               Aug 13 2004
%F A000387 Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 22 2009: 
               (Start)
%F A000387 E.g.f.: G=z^2*exp(-z)/[2(1-z)].
%F A000387 (End)
%e A000387 a(4)=6 because we have 1243, 1432, 1324, 4231, 3214, and 2134. [From 
               Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 31 2009]
%p A000387 a:=n->sum(n!*sum((-1)^k/(k-1)!, j=0..n), k=1..n): seq(-a(n)/2!, n=1..21); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 18 2007
%t A000387 Table[Subfactorial[n - 2]*Binomial[n, 2], {n, 2, 22}] [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jul 10 2009]
%Y A000387 Cf. A000240, A000449, A000475.
%Y A000387 A diagonal of A008291.
%Y A000387 a(n)+A0003221(n)=A000166(n).
%Y A000387 Sequence in context: A114959 A000386 A145221 this_sequence A027148 A095854 
               A027268
%Y A000387 Adjacent sequences: A000384 A000385 A000386 this_sequence A000388 A000389 
               A000390
%K A000387 nonn,easy
%O A000387 2,3
%A A000387 N. J. A. Sloane (njas(AT)research.att.com).