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Search: id:A000266
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| A000266 |
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Expansion of exp (-x^2 /2) / (1-x).
(Formerly M2991 N1211)
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+0
7
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| 1, 1, 1, 3, 15, 75, 435, 3045, 24465, 220185, 2200905, 24209955, 290529855, 3776888115, 52876298475, 793144477125, 12690313661025, 215735332237425, 3883235945814225, 73781482970470275, 1475629660064134575
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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For n >= 1 a(n) is the number of permutations in the symmetric group S_n such that their cycle decomposition contains no transposition.
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 85.
R. P. Stanley, Enumerative Combinatorics, Wadsworth, Vol. 1, 1986, page 93, problem 7.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 104
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FORMULA
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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
A027616(n) + a(n) = n!. - Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 09 2003
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EXAMPLE
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a(3) = 3 because the permutations in S_3 that contain no transpositions are the trivial permutation and the two 3-cycles.
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CROSSREFS
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Sequence in context: A002902 A005053 A136778 this_sequence A059838 A079164 A047015
Adjacent sequences: A000263 A000264 A000265 this_sequence A000267 A000268 A000269
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms from Christian G. Bower (bowerc(AT)usa.net).
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