Search: id:A000449
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%I A000449 M4700 N2009
%S A000449 1,0,10,40,315,2464,22260,222480,2447445,29369120,381798846,5345183480,
%T A000449 80177752655,1282844041920,21808348713320,392550276838944,7458455259940905,
%U A000449 149169105198816960,3132551209175157490,68916126601853463240
%N A000449 Rencontres numbers: permutations with exactly 3 fixed points.
%D A000449 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000449 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000449 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               65.
%F A000449 a(n)=sum((-1)^j*n!/(3!*j!), j=2..n-3).
%F A000449 For n >= 3 a(n) = C(n, 3) * A000166(n-3) = 1/6 * n! * sum((-1)^k /k!, 
               k=0..n-3). - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), 
               Apr 14 2001
%F A000449 frac 1{e^x\ (1-x)}frac{x^3}6 [From Wenjin Woan (wjwoan(AT)hotmail.com), 
               Nov 20 2008]
%p A000449 a:=n->sum(n!*sum((-1)^k/(k-2)!, j=0..n), k=2..n): seq(a(n)/3!, n=2..21); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 25 2007
%t A000449 Table[Subfactorial[n - 3]*Binomial[n, 3], {n, 3, 22}] [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jul 10 2009]
%Y A000449 Cf. A000240, A000387, A000475.
%Y A000449 A diagonal of A008291.
%Y A000449 Sequence in context: A060580 A118266 A054885 this_sequence A027274 A012868 
               A016082
%Y A000449 Adjacent sequences: A000446 A000447 A000448 this_sequence A000450 A000451 
               A000452
%K A000449 nonn,easy
%O A000449 3,3
%A A000449 N. J. A. Sloane (njas(AT)research.att.com).

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