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Search: id:A001471
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| A001471 |
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Number of degree-n permutations of order exactly 3.
(Formerly M1833 N0727)
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+0
24
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| 0, 0, 0, 2, 8, 20, 80, 350, 1232, 5768, 31040, 142010, 776600, 4874012, 27027728, 168369110, 1191911840, 7678566800, 53474964992, 418199988338, 3044269834280, 23364756531620, 199008751634000, 1605461415071822
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
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a(n) = a(n-1)+(1+a(n-3))*(n-1)(n-2) = Sum_{j = 1 to floor[n/3]}[n!/(j!*(n-3j)!*(3^j))] = A001470(n)-1 - Henry Bottomley (se16(AT)btinternet.com), Jan 26 2001.
E.g.f.: -exp(x)+exp(x+1/3*x^3).
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CROSSREFS
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Cf. A000085, A001470, A001472, A052501, A053496-A053505, A001189, A001471, A001473, A061121-A061128.
Sequence in context: A133467 A091004 A005559 this_sequence A162585 A000159 A090612
Adjacent sequences: A001468 A001469 A001470 this_sequence A001472 A001473 A001474
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)
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