Search: id:A000266
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%I A000266 M2991 N1211
%S A000266 1,1,1,3,15,75,435,3045,24465,220185,2200905,24209955,290529855,
%T A000266 3776888115,52876298475,793144477125,12690313661025,215735332237425,
%U A000266 3883235945814225,73781482970470275,1475629660064134575
%N A000266 Expansion of exp (-x^2 /2) / (1-x).
%C A000266 a(n) is the number of permutations in the symmetric group S_n whose cycle 
               decomposition contains no transposition.
%D A000266 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000266 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000266 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               85.
%D A000266 R. P. Stanley, Enumerative Combinatorics, Wadsworth, Vol. 1, 1986, page 
               93, problem 7.
%H A000266 T. D. Noe, <a href="b000266.txt">Table of n, a(n) for n=0..100</a>
%H A000266 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=104">
               Encyclopedia of Combinatorial Structures 104</a>
%F A000266 a(n) = n! * sum i=0 ... [n/2]( (-1)^i /(i! * 2^i)); a(n)/n! ~ sum i >
               = 0 (-1)^i /(i! * 2^i) = e^(-1/2); a(n) ~ e^(-1/2) * n!; a(n) ~ e^(-1/
               2) * (n/e)^n * sqrt(2 * Pi * n). - Avi Peretz (njk(AT)netvision.net.il), 
               Apr 21 2001
%F A000266 A027616(n) + a(n) = n!. - Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 
               09 2003
%e A000266 a(3) = 3 because the permutations in S_3 that contain no transpositions 
               are the trivial permutation and the two 3-cycles.
%o A000266 (PARI) {a(n) = if( n<0, 0, n! * polcoeff( exp( -(x^2 / 2) + x*O(x^n)) 
               / (1 - x), n))} /* Michael Somos Jul 28 2009 */ - Entry improved 
               by comments from Michael Somos Jul 28 2009
%Y A000266 Sequence in context: A002902 A005053 A136778 this_sequence A059838 A079164 
               A047015
%Y A000266 Adjacent sequences: A000263 A000264 A000265 this_sequence A000267 A000268 
               A000269
%K A000266 nonn
%O A000266 0,4
%A A000266 N. J. A. Sloane (njas(AT)research.att.com).
%E A000266 More terms from Christian G. Bower (bowerc(AT)usa.net).
%E A000266 Entry improved by comments from Michael Somos Jul 28 2009

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