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Search: id:A005285
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| A005285 |
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Number of permutations by inversions.
(Formerly M4414)
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+0
4
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| 1, 7, 35, 155, 649, 2640, 10569, 41926, 165425, 650658, 2554607, 10020277, 39287173, 154022930, 603919164, 2368601685, 9293159292, 36476745510, 143239635450, 562744102479, 2211876507387, 8697839966552, 34218338900591
(list; graph; listen)
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OFFSET
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7,2
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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).
R. K. Guy, personal communication.
R. H. Moritz and R. C. Williams, A coin-tossing problem and some related combinatorics, Math. Mag., 61 (1988), 24-29.
E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 96.
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LINKS
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B. H. Margolius, Permutations with inversions, J. Integ. Seqs. Vol. 4 (2001), #01.2.4.
Lalit Jain and Pavlos Tzermias, Beukers' integrals and Apery's recurrences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.1.1.
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FORMULA
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a(n)=2^{2n+6}/sqrt{pi n}Q(1+O(n^{-1})) where Q is a digital search tree constant, Q = 0.2887880951...
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MAPLE
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g := proc(n, k) option remember; if k=0 then return(1) else if (n=1 and k=1) then return(0) else if (k<0 or k>binomial(n, 2)) then return(0) else g(n-1, k)+g(n, k-1)-g(n-1, k-n) end if end if end if end proc; seq(g(j+7, j), j=0..30);
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CROSSREFS
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Cf. A008302, A005283, A005284.
Sequence in context: A094825 A022635 A000588 this_sequence A006095 A005003 A163348
Adjacent sequences: A005282 A005283 A005284 this_sequence A005286 A005287 A005288
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KEYWORD
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nonn
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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, Maple code, asymptotic formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 5/31/01
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