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Search: id:A000090
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| A000090 |
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E.g.f. exp((-x^3)/3)/(1-x).
(Formerly M1295 N0496)
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+0
5
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| 1, 1, 2, 4, 16, 80, 520, 3640, 29120, 259840, 2598400, 28582400, 343235200, 4462057600, 62468806400, 936987251200, 14991796019200, 254860532326400, 4587501779660800, 87162533813555200, 1743250676271104000
(list; graph; listen)
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OFFSET
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0,3
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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 3-cycle.
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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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Christian G. Bower, Table of n, a(n) for n=0..100
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FORMULA
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a(n) = n! * sum i=0 ... [n/3]( (-1)^i /(i! * 3^i)); a(n)/n! ~ sum i >= 0 (-1)^i /(i! * 3^i) = e^(-1/3); a(n) ~ e^(-1/3) * n!; a(n) ~ e^(-1/3) * (n/e)^n * sqrt(2 * Pi * n). - Avi Peretz (njk(AT)netvision.net.il), Apr 22 2001
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EXAMPLE
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a(3) = 4 because the permutations in S_3 that contain no 3-cycles are the trivial permutation and the 3 transpositions.
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MAPLE
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seq(coeff(convert(series(exp((-x^3)/3)/(1-x), x, 50), polynom), x, i)*i!, i=0..30); # series expansion A000090:=n->n!*add((-1)^i/(i!*3^i), i=0..floor(n/3)); seq(A000090(n), n=0..30); # formula (Pab Ter)
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CROSSREFS
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Cf. A000142, A000138.
Adjacent sequences: A000087 A000088 A000089 this_sequence A000091 A000092 A000093
Sequence in context: A025225 A115125 A000831 this_sequence A013115 A007171 A058136
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 22 2005
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